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0.478 w 0 0 m 4.234 0 l S Q BT /F16 7.9701 Tf 487.781 347.282 Td [(2)]TJ/F15 11.9552 Tf 8.257 4.123 Td [(\050b)-27(ecause)]TJ/F17 5.9776 Tf -421.647 -8.972 Td [(3)]TJ ET q 1 0 0 1 74.391 341.168 cm []0 d 0 J 0.359 w 0 0 m 3.653 0 l S Q BT /F17 5.9776 Tf 74.391 336.049 Td [(2)]TJ ET q 1 0 0 1 73.196 335.332 cm []0 d 0 J 0.478 w 0 0 m 6.044 0 l S Q BT /F17 5.9776 Tf 74.391 330.763 Td [(1)]TJ ET q 1 0 0 1 74.391 329.497 cm []0 d 0 J 0.359 w 0 0 m 3.653 0 l S Q BT /F17 5.9776 Tf 74.391 324.379 Td [(2)]TJ/F15 11.9552 Tf 9.514 7.964 Td [(=)-290(3,)-336(an)-333(in)27(teger\051,)-335(but)-334(according)-334(to)-333(the)-334(\014rst)-333(de\014nition)]TJ/F16 7.9701 Tf 275.122 4.707 Td [(3)]TJ ET q 1 0 0 1 359.027 335.332 cm []0 d 0 J 0.478 w 0 0 m 4.234 0 l S Q BT /F16 7.9701 Tf 359.027 328.221 Td [(2)]TJ/F15 11.9552 Tf 9.419 4.122 Td [(is)-334(not)-333(divisible)-334(b)27(y)]TJ/F16 7.9701 Tf 96.299 4.707 Td [(1)]TJ ET q 1 0 0 1 464.745 335.332 cm []0 d 0 J 0.478 w 0 0 m 4.234 0 l S Q BT /F16 7.9701 Tf 464.745 328.221 Td [(2)]TJ/F15 11.9552 Tf 9.419 4.122 Td [(b)-27(ecause)-334(they)]TJ -402.164 -17.263 Td [(are)-447(not)-447(in)27(tegers.)-797(Because)-447(these)-447(de\014ni)1(tions)-447(ha)27(v)27(e)-447(di\013eren)27(t)-447(example)1(s)-1(,)-477(they)-447(de\014ne)-447(di)1(\013eren)27(t)]TJ 0 -14.446 Td [(concepts)-440(and)-441(t)1(hey)-441(are)-440(di\013eren)27(t)-440(de\014nitions.)-777(There)-440(ma)27(y)-440(b)-27(e)-441(other)-440(di\013ering)-440(examples)-440(than)]TJ 0 -14.446 Td [(these.)]TJ ET 1 0 0 1 89.559 260.288 cm EMC /P <> BDC 1 0 0 1 -89.559 -260.288 cm BT /F15 11.9552 Tf 89.559 260.288 Td [(3.6)-326(De\014ne)-327(what)-326(it)-326(means)-327(for)-326(an)-326(in)27(teger)-326(to)-327(b)-27(e)-326(a)-327(squ)1(are.)]TJ ET 1 0 0 1 89.559 245.843 cm EMC /P <> BDC 1 0 0 1 -89.559 -245.843 cm BT /F15 11.9552 Tf 89.559 245.843 Td [(An)-326(in)27(teger)]TJ/F18 11.9552 Tf 57.875 0 Td [(x)]TJ/F15 11.9552 Tf 10.554 0 Td [(is)-326(called)-327(square)-326(pro)27(vided)-326(there)-326(exists)-327(an)-326(in)27(teger)]TJ/F18 11.9552 Tf 247.062 0 Td [(r)]TJ/F15 11.9552 Tf 9.502 0 Td [(suc)27(h)-326(that)]TJ/F18 11.9552 Tf 51.767 0 Td [(r)]TJ/F16 7.9701 Tf 5.6 4.338 Td [(2)]TJ/F15 11.9552 Tf 8.053 -4.338 Td [(=)]TJ/F18 11.9552 Tf 12.426 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(.)]TJ ET 1 0 0 1 89.559 219.942 cm EMC /P <> BDC 1 0 0 1 -89.559 -219.942 cm BT /F15 11.9552 Tf 89.559 219.942 Td [([extra])-384(3.8)-383(This)-384(is)-384(a)-383(little)-384(tric)27(ky)82(,)-398(b)-27(ecause)-384(w)27(e're)-383(not)-384(quite)-384(sure)-383(ho)27(w)-384(a)-384(p)-27(olygon)-383(has)-384(b)-27(een)]TJ -17.559 -14.445 Td [(de\014ned)-424(\050and)-425(de\014ning)-424(a)-425(p)-27(olygon)-424(is)-425(v)27(ery)-424(tric)27(ky)82(,)-449(if)-425(y)27(ou)-424(think)-425(ab)-27(out)-424(it\051.)-730(Here)-425(is)-424(a)-425(p)-27(olygon)]TJ 0 -14.446 Td 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[(b)-27(e)-363(the)-362(distance)-363(\134around",)-372(since)-362(that)-363(is)-362(not)-363(de\014ned.)-544(Bey)27(ond)-362(that,)-372(this)-363(is)]TJ -92.485 -14.445 Td [(not)-326(a)-327(particular)1(ly)-327(c)27(hallen)1(ging)-327(question.)-435(Consider)-326(3.10)-326(and)-327(3.6)-326(nearb)27(y)-326(for)-326(others.)]TJ ET 1 0 0 1 89.559 92.922 cm EMC /P <> BDC 1 0 0 1 -89.559 -92.922 cm BT /F15 11.9552 Tf 89.559 92.922 Td [([extra])-232(3.10)-233(A)-232(p)-27(oin)27(t)-232(on)-233(a)-232(line)-233(segm)1(en)27(t)-233(is)-232(the)-232(midp)-28(oin)28(t)-233(if)-232(it)-233(is)-232(equidistan)27(t)-232(to)-232(b)-28(oth)-232(endp)-27(oin)27(ts.)]TJ/F27 11.9552 Tf -17.559 -14.446 Td [(or)]TJ/F15 11.9552 Tf 14.632 0 Td [(The)-311(p)-28(o)1(in)27(t)]TJ/F18 11.9552 Tf 54.27 0 Td [(C)]TJ/F15 11.9552 Tf 12.957 0 Td [(is)-311(the)-312(midp)-27(oin)27(t)-311(of)-311(line)-312(segmen)28(t)]TJ/F18 11.9552 Tf 161.638 0 Td [(AB)]TJ/F15 11.9552 Tf 21.995 0 Td [(if)]TJ/F18 11.9552 Tf 10.551 0 Td [(C)]TJ/F15 11.9552 Tf 12.957 0 Td [(is)-311(on)-312(segmen)28(t)]TJ/F18 11.9552 Tf 72.755 0 Td [(AB)]TJ/F15 11.9552 Tf 21.995 0 Td [(and)-311(the)-312(distance)]TJ -383.75 -14.446 Td [(from)]TJ/F18 11.9552 Tf 27.815 0 Td [(A)]TJ/F15 11.9552 Tf 12.853 0 Td [(to)]TJ/F18 11.9552 Tf 14.483 0 Td [(C)]TJ/F15 11.9552 Tf 13.312 0 Td [(is)-341(equal)-341(to)-341(the)-341(distance)-341(from)]TJ/F18 11.9552 Tf 151.411 0 Td [(B)]TJ/F15 11.9552 Tf 13.574 0 Td [(to)]TJ/F18 11.9552 Tf 14.484 0 Td [(C)]TJ/F15 11.9552 Tf 9.233 0 Td [(.)-479(Most)-341(imp)-28(o)1(rtan)27(tly:)-465(mak)28(e)-342(sur)1(e)-342(tha)1(t)]TJ/F18 11.9552 Tf 189.655 0 Td [(C)]TJ/F15 11.9552 Tf 13.311 0 Td [(is)]TJ/F27 11.9552 Tf -460.131 -14.446 Td [(on)]TJ/F15 11.9552 Tf 16.937 0 Td [(the)-367(segme)1(n)27(t.)-556(Instead)-367(of)-367(e)1(mphasising)]TJ/F27 11.9552 Tf 193.849 0 Td [(on)]TJ/F15 11.9552 Tf 12.553 0 Td [(,)-377(it)-366(do)-28(e)1(s)-367(su\016ce)-367(to)-366(sa)27(y)-367(that)]TJ/F18 11.9552 Tf 143.833 0 Td [(C)]TJ/F15 11.9552 Tf 13.617 0 Td [(is)]TJ/F27 11.9552 Tf 12.253 0 Td [(b)50(etwe)50(en)]TJ/F18 11.9552 Tf 42.939 0 Td [(A)]TJ/F15 11.9552 Tf 13.159 0 Td [(and)]TJ/F18 11.9552 Tf -449.14 -14.446 Td [(B)]TJ/F15 11.9552 Tf 9.496 0 Td [(.)-435(Some)-326(e\013ort)-327(should)-326(also)-326(b)-28(e)-326(mak)27(e)-326(to)-326(k)27(eep)-326(the)-327(writing)-326(clear)-326(and)-327(unclu)1(ttered.)]TJ ET 1 0 0 1 72 35.138 cm EMC endstream endobj 56 0 obj << /Length 13670 >> stream 1 0 0 1 72 683.138 cm /P <> BDC 1 0 0 1 17.559 -11.955 cm EMC /P <> BDC 1 0 0 1 -89.559 -671.183 cm BT /F15 11.9552 Tf 89.559 671.183 Td [(4.3.)-431(Find)-316(t)28(w)27(o)-316(con)1(ditions)-316(A)-315(and)-315(B)-316(suc)28(h)-316(that)-315(\050a\051)-315(If)-316(A)-315(then)-315(B.)-316(is)-315(true)-315(but)-315(\050b\051)-316(if)-315(B)-315(then)-316(A.)]TJ -17.559 -14.446 Td [(is)-326(false.)]TJ ET 1 0 0 1 114.727 656.737 cm EMC 1 0 0 1 -13.462 -24.408 cm /Quote <> BDC 1 0 0 1 -101.265 -632.329 cm BT /F15 11.9552 Tf 101.265 632.329 Td [(Consider)-326(A:)-327(It)-326(is)-326(300)]TJ/F19 7.9701 Tf 106.776 4.338 Td [(o)]TJ/F15 11.9552 Tf 8.493 -4.338 Td [(F)-326(and)-327(B:)-326(W)81(a)1(ter)-327(is)-326(b)-27(oiling.)]TJ ET 1 0 0 1 356.413 632.329 cm EMC 1 0 0 1 -284.413 -24.409 cm /P <> BDC 1 0 0 1 -72 -607.92 cm BT /F15 11.9552 Tf 72 607.92 Td [(It)-295(is)-295(true)-294(that)-295(If)-295(it)-295(is)-295(300)]TJ/F19 7.9701 Tf 124.62 4.339 Td [(o)]TJ/F15 11.9552 Tf 8.116 -4.339 Td [(F)-295(then)-294(w)27(ater)-295(is)-295(b)-27(oiling.)-295(It)-294(is)-295(false)-295(that)-295(If)-295(w)28(ater)-295(is)-295(b)-27(oiling)-295(then)-295(it)-294(is)]TJ -132.736 -14.446 Td [(300)]TJ/F19 7.9701 Tf 17.559 4.339 Td [(o)]TJ/F15 11.9552 Tf 7.882 -4.339 Td [(F)-275(as)-276(it)-275(could)-275(b)-27(e)-275(man)27(y)-275(other)-276(temp)-27(eratures.)-418(Of)-275(course,)-285(there)-276(are)-275(man)27(y)-275(p)-27(ossible)-275(examples)]TJ -25.441 -14.445 Td [(here.)]TJ ET 1 0 0 1 89.559 552.628 cm EMC /P <> BDC 1 0 0 1 -89.559 -552.628 cm BT /F15 11.9552 Tf 89.559 552.628 Td [(4.10.)-428(Is)-306(the)-306(claim)-305(If)-306(y)27(ou)-306(pic)28(k)-306(a)-306(guinea)-305(pig)-306(up)-306(b)27(y)-305(its)-306(tail,)-310(then)-306(its)-305(ey)27(es)-306(will)-306(p)-27(op)-305(out.)-306(true?)]TJ ET 1 0 0 1 89.559 538.182 cm EMC /P <> BDC 1 0 0 1 -89.559 -538.182 cm BT /F15 11.9552 Tf 89.559 538.182 Td [(Based)-294(on)-295(the)-294(photo)-295(in)-294(the)-294(hin)27(ts,)-301(it)-294(lo)-28(oks)-294(as)-295(if)-294(y)27(ou)-294(cannot)-295(pic)28(k)-295(up)-294(a)-295(guinea)-294(pig)-294(b)27(y)-295(its)-294(tail.)]TJ -17.559 -14.446 Td [(Therefore,)-326(the)-327(h)28(yp)-27(othesis)-327(is)-326(v)54(acuous)-326(\050alw)27(a)27(y)1(s)-327(false\051)-326(and)-327(so)-326(the)-326(statemen)27(t)-326(is)-327(true.)]TJ ET 1 0 0 1 89.559 497.335 cm EMC /P <> BDC 1 0 0 1 -89.559 -497.335 cm BT /F15 11.9552 Tf 89.559 497.335 Td [(5.2.)-435(Pro)27(v)27(e)-326(that)-326(the)-327(sum)-326(of)-326(an)-327(o)-27(dd)-326(in)27(teger)-326(and)-327(an)-326(ev)27(en)-326(in)27(teger)-326(is)-326(o)-28(dd.)]TJ ET 1 0 0 1 89.559 482.889 cm EMC /P <> BDC 1 0 0 1 -89.559 -482.889 cm BT /F15 11.9552 Tf 89.559 482.889 Td [(This)-326(can)-327(b)-27(e)-326(restated)-326(as)]TJ ET 1 0 0 1 72 482.889 cm EMC 1 0 0 1 29.265 -27.397 cm /Quote <> BDC 1 0 0 1 -101.265 -455.492 cm BT /F15 11.9552 Tf 101.265 455.492 Td [(If)]TJ/F18 11.9552 Tf 11.702 0 Td [(a)]TJ/F15 11.9552 Tf 10.047 0 Td [(is)-326(an)-327(o)-27(dd)-326(in)27(teger)-326(and)]TJ/F18 11.9552 Tf 112.572 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(is)-326(an)-327(ev)27(e)1(n)-327(in)27(teger)-326(then)]TJ/F18 11.9552 Tf 120.052 0 Td [(a)]TJ/F15 11.9552 Tf 8.801 0 Td [(+)]TJ/F18 11.9552 Tf 11.762 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(is)-326(o)-28(dd)1(.)]TJ ET 1 0 0 1 433.369 455.492 cm EMC 1 0 0 1 -343.81 -27.397 cm /P <> BDC 1 0 0 1 -89.559 -428.095 cm BT /F15 11.9552 Tf 89.559 428.095 Td [(Supp)-27(ose)-366(that)]TJ/F18 11.9552 Tf 72.213 0 Td [(a)]TJ/F15 11.9552 Tf 10.515 0 Td [(is)-366(a)1(n)-366(o)-27(dd)-366(in)28(teger.)-553(By)-365(de\014nition)-366(of)-365(o)-28(d)1(d,)]TJ/F18 11.9552 Tf 209.228 0 Td [(a)]TJ/F15 11.9552 Tf 10.262 0 Td [(=)-344(2)]TJ/F18 11.9552 Tf 19.075 0 Td [(x)]TJ/F15 11.9552 Tf 9.628 0 Td [(+)-249(1)-365(for)-366(some)-365(in)27(teger)]TJ/F18 11.9552 Tf 109.616 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(.)]TJ -464.748 -14.446 Td [(Supp)-27(ose)-323(that)]TJ/F18 11.9552 Tf 71.192 0 Td [(b)]TJ/F15 11.9552 Tf 8.837 0 Td [(is)-323(an)-323(ev)28(en)-323(in)27(teger.)-434(By)-323(de\014nition)-322(of)-323(ev)27(en,)]TJ/F18 11.9552 Tf 211.283 0 Td [(b)]TJ/F15 11.9552 Tf 8.837 0 Td [(is)-323(divisible)-323(b)28(y)-323(2.)-434(By)-323(de\014nition)-323(of)]TJ -300.149 -14.446 Td [(divisible,)]TJ/F18 11.9552 Tf 48.32 0 Td [(b)]TJ/F15 11.9552 Tf 8.298 0 Td [(=)-278(2)]TJ/F18 11.9552 Tf 18.279 0 Td [(c)]TJ/F15 11.9552 Tf 7.884 0 Td [(for)-238(some)-238(in)27(teger)]TJ/F18 11.9552 Tf 82.741 0 Td [(c)]TJ/F15 11.9552 Tf 5.038 0 Td [(.)-406(Consider)]TJ/F18 11.9552 Tf 55.887 0 Td [(a)]TJ/F15 11.9552 Tf 6.645 0 Td [(+)]TJ/F18 11.9552 Tf 9.604 0 Td [(b)]TJ/F15 11.9552 Tf 8.298 0 Td [(=)-278(\0502)]TJ/F18 11.9552 Tf 22.831 0 Td [(x)]TJ/F15 11.9552 Tf 7.152 0 Td [(+)-42(1\051)-42(+)-41(\0502)]TJ/F18 11.9552 Tf 40.52 0 Td [(c)]TJ/F15 11.9552 Tf 5.038 0 Td [(\051)-278(=)-277(2)]TJ/F18 11.9552 Tf 26.152 0 Td [(x)]TJ/F15 11.9552 Tf 7.152 0 Td [(+)-42(2)]TJ/F18 11.9552 Tf 15.457 0 Td [(c)]TJ/F15 11.9552 Tf 5.538 0 Td [(+)-42(1)-278(=)-277(2\050)]TJ/F18 11.9552 Tf 41.61 0 Td [(x)]TJ/F15 11.9552 Tf 7.152 0 Td [(+)]TJ/F18 11.9552 Tf 9.604 0 Td [(c)]TJ/F15 11.9552 Tf 5.038 0 Td [(\051)-42(+)-42(1.)]TJ -444.238 -14.446 Td [(\050This)-433(uses)-432(substitution,)-459(asso)-27(ciativit)27(y)82(,)-460(comm)28(utativit)27(y)82(,)-460(an)1(d)-433(distribution,)-459(all)-433(items)-432(assumed)]TJ 0 -14.446 Td [(from)-341(App)-27(endix)-340(D.\051)-341(W)82(e)-341(also)-341(k)1(no)27(w)-341(that)-340(the)-341(in)27(tegers)-340(are)-341(closed)-340(under)-341(addition,)-344(so)-341(if)]TJ/F18 11.9552 Tf 429.305 0 Td [(x)]TJ/F15 11.9552 Tf 10.725 0 Td [(and)]TJ/F18 11.9552 Tf 22.932 0 Td [(c)]TJ/F15 11.9552 Tf -462.962 -14.445 Td [(are)-372(in)27(tegers,)-384(t)1(hen)]TJ/F18 11.9552 Tf 94.518 0 Td [(x)]TJ/F15 11.9552 Tf 9.682 0 Td [(+)]TJ/F18 11.9552 Tf 12.135 0 Td [(c)]TJ/F15 11.9552 Tf 9.488 0 Td [(is)-372(also)-372(an)-373(in)28(teger.)-573(Then,)]TJ/F18 11.9552 Tf 132.543 0 Td [(x)]TJ/F15 11.9552 Tf 9.682 0 Td [(+)]TJ/F18 11.9552 Tf 12.134 0 Td [(c)]TJ/F15 11.9552 Tf 9.488 0 Td [(is)-372(the)-372(desired)-373(in)28(teger,)]TJ/F18 11.9552 Tf 115.942 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(,)-384(suc)28(h)-373(that)]TJ/F18 11.9552 Tf -411.749 -14.446 Td [(a)]TJ/F15 11.9552 Tf 8.802 0 Td [(+)]TJ/F18 11.9552 Tf 11.761 0 Td [(b)]TJ/F15 11.9552 Tf 8.298 0 Td [(=)-278(2)]TJ/F18 11.9552 Tf 18.278 0 Td [(y)]TJ/F15 11.9552 Tf 8.794 0 Td [(+)-222(1.)-435(Therefore,)-326(b)27(y)-327(de\014ni)1(tion)-327(of)-326(o)-27(dd,)]TJ/F18 11.9552 Tf 190.277 0 Td [(a)]TJ/F15 11.9552 Tf 8.802 0 Td [(+)]TJ/F18 11.9552 Tf 11.761 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(is)-326(o)-28(dd,)-326(as)-326(desired.)]TJ ET 1 0 0 1 89.559 315.019 cm EMC /P <> BDC 1 0 0 1 -89.559 -315.019 cm BT /F15 11.9552 Tf 89.559 315.019 Td [(5.12.)-435(Supp)-27(ose)]TJ/F18 11.9552 Tf 75.178 0 Td [(a;)-167(b;)-166(c)]TJ/F15 11.9552 Tf 26.649 0 Td [(,)-326(and)]TJ/F18 11.9552 Tf 29.915 0 Td [(d)]TJ/F15 11.9552 Tf 9.985 0 Td [(are)-326(in)27(tegers.)-435(Pro)27(v)27(e)-326(that)-326(if)]TJ/F18 11.9552 Tf 136.47 0 Td [(a)]TJ/F21 11.9552 Tf 9.466 0 Td [(j)]TJ/F18 11.9552 Tf 6.641 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(and)]TJ/F18 11.9552 Tf 22.762 0 Td [(c)]TJ/F21 11.9552 Tf 8.359 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(d)]TJ/F15 11.9552 Tf 6.082 0 Td [(,)-326(then)-327(\050)]TJ/F18 11.9552 Tf 38.37 0 Td [(ac)]TJ/F15 11.9552 Tf 11.183 0 Td [(\051)]TJ/F21 11.9552 Tf 7.873 0 Td [(j)]TJ/F15 11.9552 Tf 6.642 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(bd)]TJ/F15 11.9552 Tf 11.06 0 Td [(\051.)]TJ ET 1 0 0 1 89.559 300.573 cm EMC /P <> BDC 1 0 0 1 -89.559 -300.573 cm BT /F15 11.9552 Tf 89.559 300.573 Td [(Supp)-27(ose)-326(that)]TJ/F18 11.9552 Tf 71.276 0 Td [(a)]TJ/F21 11.9552 Tf 9.466 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(.)-435(By)-327(d)1(e\014nition)-327(of)]TJ/F21 11.9552 Tf 92.182 0 Td [(j)]TJ/F15 11.9552 Tf 3.321 0 Td [(,)-326(there)-327(is)-326(an)-326(in)27(teger)]TJ/F18 11.9552 Tf 103.793 0 Td [(m)]TJ/F15 11.9552 Tf 14.142 0 Td [(suc)27(h)-326(that)]TJ/F18 11.9552 Tf 51.766 0 Td [(b)]TJ/F15 11.9552 Tf 8.298 0 Td [(=)]TJ/F18 11.9552 Tf 12.425 0 Td [(am)]TJ/F15 11.9552 Tf 16.385 0 Td [(.)]TJ ET 1 0 0 1 89.559 286.127 cm EMC /P <> BDC 1 0 0 1 -89.559 -286.127 cm BT /F15 11.9552 Tf 89.559 286.127 Td [(Supp)-27(ose)-326(that)]TJ/F18 11.9552 Tf 71.276 0 Td [(c)]TJ/F21 11.9552 Tf 8.359 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(d)]TJ/F15 11.9552 Tf 6.083 0 Td [(.)-435(By)-326(de\014nition)-327(of)]TJ/F21 11.9552 Tf 92.182 0 Td [(j)]TJ/F15 11.9552 Tf 3.321 0 Td [(,)-326(there)-327(is)-326(an)-326(in)27(teger)]TJ/F18 11.9552 Tf 103.793 0 Td [(n)]TJ/F15 11.9552 Tf 10.89 0 Td [(suc)27(h)-326(that)]TJ/F18 11.9552 Tf 51.766 0 Td [(d)]TJ/F15 11.9552 Tf 9.404 0 Td [(=)]TJ/F18 11.9552 Tf 12.425 0 Td [(cn)]TJ/F15 11.9552 Tf 12.026 0 Td [(.)]TJ ET 1 0 0 1 89.559 271.681 cm EMC /P <> BDC 1 0 0 1 -89.559 -271.681 cm BT /F15 11.9552 Tf 89.559 271.681 Td [(Therefore,)]TJ/F18 11.9552 Tf 58.168 0 Td [(bd)]TJ/F15 11.9552 Tf 16.988 0 Td [(=)-496(\050)]TJ/F18 11.9552 Tf 19.584 0 Td [(am)]TJ/F15 11.9552 Tf 16.384 0 Td [(\051\050)]TJ/F18 11.9552 Tf 9.105 0 Td [(cn)]TJ/F15 11.9552 Tf 12.026 0 Td [(\051)-496(=)]TJ/F18 11.9552 Tf 25.512 0 Td [(ac)]TJ/F15 11.9552 Tf 11.183 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(mn)]TJ/F15 11.9552 Tf 17.227 0 Td [(\051)-454(b)27(y)-455(substition,)-486(comm)27(utativit)28(y)81(,)-486(and)-455(asso)-27(ciativit)27(y)82(.)]TJ -208.288 -14.446 Td [(Because)-295(the)-296(in)28(tegers)-296(are)-295(closed)-295(under)-295(m)27(ultiplication,)]TJ/F18 11.9552 Tf 271.297 0 Td [(mn)]TJ/F15 11.9552 Tf 20.758 0 Td [(is)-295(an)-296(in)28(teger)-296(and)-295(therefore)-295(satis\014es)]TJ -292.055 -14.445 Td [(the)-326(de\014nition)-327(o)1(f)-327(divisibilit)27(y)-326(so)-326(that)]TJ/F18 11.9552 Tf 182.873 0 Td [(ac)]TJ/F21 11.9552 Tf 14.504 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(bd)]TJ/F15 11.9552 Tf 11.06 0 Td [(,)-326(as)-327(desired.)]TJ ET 1 0 0 1 89.559 216.389 cm EMC /P <> BDC 1 0 0 1 -89.559 -216.389 cm BT /F15 11.9552 Tf 89.559 216.389 Td [(5.15.)-435(Let)]TJ/F18 11.9552 Tf 50.236 0 Td [(x)]TJ/F15 11.9552 Tf 10.554 0 Td [(b)-27(e)-327(an)-326(in)27(teger.)-435(Pro)28(v)27(e)-327(that)-326(0)]TJ/F21 11.9552 Tf 142.978 0 Td [(j)]TJ/F18 11.9552 Tf 6.641 0 Td [(x)]TJ/F15 11.9552 Tf 10.555 0 Td [(if)-326(and)-327(only)-326(if)-326(x)-327(=)-326(0.)]TJ ET 1 0 0 1 89.559 201.943 cm EMC /P <> BDC 1 0 0 1 -89.559 -201.943 cm BT /F15 11.9552 Tf 89.559 201.943 Td [(In)-326(t)27(w)27(o)-326(directions)-327(-)-326(pro)27(v)28(e)]TJ ET 1 0 0 1 219.036 201.943 cm EMC 1 0 0 1 -117.771 -24.409 cm /Quote <> BDC 1 0 0 1 -101.265 -177.534 cm BT /F15 11.9552 Tf 101.265 177.534 Td [(if)-326(0)]TJ/F21 11.9552 Tf 19.904 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(x)]TJ/F15 11.9552 Tf 10.554 0 Td [(then)]TJ/F18 11.9552 Tf 26.664 0 Td [(x)]TJ/F15 11.9552 Tf 9.973 0 Td [(=)-278(0,)-326(and)-326(if)]TJ/F18 11.9552 Tf 58.924 0 Td [(x)]TJ/F15 11.9552 Tf 9.973 0 Td [(=)-278(0)-326(then)-326(0)]TJ/F21 11.9552 Tf 58.018 0 Td [(j)]TJ/F18 11.9552 Tf 6.641 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(.)]TJ ET 1 0 0 1 323.665 177.534 cm EMC 1 0 0 1 -234.106 -24.408 cm /P <> BDC 1 0 0 1 -89.559 -153.126 cm BT /F15 11.9552 Tf 89.559 153.126 Td [(If)-331(0)]TJ/F21 11.9552 Tf 21.021 0 Td [(j)]TJ/F18 11.9552 Tf 6.733 0 Td [(x)]TJ/F15 11.9552 Tf 10.608 0 Td [(then)-331(there)-331(is)-330(an)-331(in)27(teger)]TJ/F18 11.9552 Tf 123.571 0 Td [(c)]TJ/F15 11.9552 Tf 8.994 0 Td [(suc)27(h)-331(that)-330(0\050)]TJ/F18 11.9552 Tf 62.279 0 Td [(c)]TJ/F15 11.9552 Tf 5.038 0 Td [(\051)-285(=)]TJ/F18 11.9552 Tf 20.481 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(.)-449(But)-330(then)-331(b)27(y)-331(m)27(ultiplicat)1(ion,)]TJ/F18 11.9552 Tf 153.378 0 Td [(x)]TJ/F15 11.9552 Tf 10.064 0 Td [(=)-285(0,)]TJ -446.378 -14.446 Td [(as)-326(desired.)]TJ ET 1 0 0 1 89.559 124.234 cm EMC /P <> BDC 1 0 0 1 -89.559 -124.234 cm BT /F15 11.9552 Tf 89.559 124.234 Td [(If)]TJ/F18 11.9552 Tf 11.702 0 Td [(x)]TJ/F15 11.9552 Tf 9.973 0 Td [(=)-278(0,)-326(sho)27(wing)-326(0)]TJ/F21 11.9552 Tf 79.218 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(x)]TJ/F15 11.9552 Tf 10.554 0 Td [(is)-326(only)-327(sho)28(wing)-327(0)]TJ/F21 11.9552 Tf 91.246 0 Td [(j)]TJ/F15 11.9552 Tf 6.642 0 Td [(0.)-435(This)-326(is)-327(true)-326(b)-27(ecause)-327(0)-326(\05083456\051)-326(=)-327(0.)]TJ ET 1 0 0 1 89.559 97.833 cm EMC /P <> BDC 1 0 0 1 -89.559 -97.833 cm BT /F15 11.9552 Tf 89.559 97.833 Td [([extra])-313(5.21)-313(Pro)27(v)27(e)-313(that)-313(the)-313(di\013erence)-313(b)-27(et)27(w)27(een)-313(distinct,)-316(nonconsecutiv)28(e)-314(p)-27(erfect)-313(squares)-313(is)]TJ -17.559 -14.446 Td [(comp)-27(osite.)-435(This)-327(ca)1(n)-327(b)-27(e)-326(restated)-327(as)]TJ ET 1 0 0 1 72 81.063 cm EMC 1 0 0 1 29.265 -25.073 cm /Quote <> BDC 1 0 0 1 -101.265 -55.99 cm BT /F15 11.9552 Tf 101.265 55.99 Td [(If)]TJ/F18 11.9552 Tf 11.702 0 Td [(x)]TJ/F15 11.9552 Tf 10.554 0 Td [(and)]TJ/F18 11.9552 Tf 22.762 0 Td [(y)]TJ/F15 11.9552 Tf 10.038 0 Td [(are)-326(distinct)-327(and)-326(nonconsecutiv)28(e)-327(in)27(tegers,)-326(then)]TJ/F18 11.9552 Tf 238.542 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 7.389 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.955 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 8.634 -4.338 Td [(is)-326(comp)-27(osite.)]TJ ET 1 0 0 1 506.972 55.99 cm EMC endstream endobj 71 0 obj << /Length 15010 >> stream 1 0 0 1 89.559 671.183 cm /P <> BDC 1 0 0 1 -89.559 -671.183 cm BT /F15 11.9552 Tf 89.559 671.183 Td [(Supp)-27(ose)-330(that)]TJ/F18 11.9552 Tf 71.355 0 Td [(x)]TJ/F15 11.9552 Tf 10.593 0 Td [(and)]TJ/F18 11.9552 Tf 22.801 0 Td [(y)]TJ/F15 11.9552 Tf 10.078 0 Td [(are)-330(distinct)-329(and)-330(nonconsecutiv)28(e)-330(in)27(tegers)-329(.)-445(Since)-330(they)-330(are)-329(distinct,)]TJ -132.386 -14.446 Td [(one)-435(m)27(ust)-435(b)-27(e)-435(larger.)-762(Because)-435(the)-435(v)54(aria)1(bles)-436(are)-435(meaningless)-435(b)-27(efore)-435(hand,)-462(supp)-27(ose)]TJ/F18 11.9552 Tf 431.786 0 Td [(x)-463(>)-463(y)]TJ/F15 11.9552 Tf 32.962 0 Td [(.)]TJ -464.748 -14.446 Td [(Because)-273(they)-272(are)-273(nonconsecutiv)28(e,)-284(in)-272(fact,)-284(w)28(e)-273(ma)27(y)-273(f)1(urther)-273(supp)-27(ose)]TJ/F18 11.9552 Tf 334.38 0 Td [(x)-278(>)-278(y)]TJ/F15 11.9552 Tf 29.88 0 Td [(+)-113(1)1(.)-418(T)82(o)-273(sho)27(w)]TJ/F18 11.9552 Tf 69.498 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.339 Td [(2)]TJ/F21 11.9552 Tf 6.077 -4.339 Td [(\000)]TJ/F18 11.9552 Tf 10.644 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.339 Td [(2)]TJ/F15 11.9552 Tf -463.268 -18.784 Td [(is)-279(comp)-27(osite,)-288(b)27(y)-278(de\014nition,)-288(w)27(e)-279(m)27(ust)-278(sho)27(w)-279(that)-278(there)-279(is)-279(a)1(n)-279(in)27(teger)]TJ/F18 11.9552 Tf 332.207 0 Td [(b)]TJ/F15 11.9552 Tf 8.309 0 Td [(suc)27(h)-278(that)-279(1)]TJ/F18 11.9552 Tf 59.8 0 Td [(<)-278(b)-277(<)-278(x)]TJ/F16 7.9701 Tf 39.801 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.224 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 10.79 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf -463.268 -18.784 Td [(and)]TJ/F18 11.9552 Tf 22.46 0 Td [(b)]TJ/F21 11.9552 Tf 4.977 0 Td [(j)]TJ/F18 11.9552 Tf 3.321 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.773 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.339 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 4.732 -4.338 Td [(.)-427(Notice)-301(that)]TJ/F18 11.9552 Tf 69.853 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.773 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.339 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 8.053 -4.338 Td [(=)-278(\050)]TJ/F18 11.9552 Tf 16.978 0 Td [(x)]TJ/F21 11.9552 Tf 8.692 0 Td [(\000)]TJ/F18 11.9552 Tf 11.339 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051\050)]TJ/F18 11.9552 Tf 9.105 0 Td [(x)]TJ/F15 11.9552 Tf 8.692 0 Td [(+)]TJ/F18 11.9552 Tf 11.146 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051,)-306(so)-301(\050)]TJ/F18 11.9552 Tf 30.088 0 Td [(x)]TJ/F21 11.9552 Tf 8.693 0 Td [(\000)]TJ/F18 11.9552 Tf 11.339 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051)]TJ/F21 11.9552 Tf 4.553 0 Td [(j)]TJ/F15 11.9552 Tf 3.32 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.773 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.339 0 Td [(y)]TJ/F16 7.9701 Tf 6.136 4.338 Td [(2)]TJ/F15 11.9552 Tf 4.733 -4.338 Td [(\051.)-427(W)82(e)-301(need)-301(only)-301(sho)27(w)]TJ -357.738 -14.446 Td [(that)-349(one)-349(of)-350(the)-349(factors)-349(is)-350(the)-349(appropriate)-349(size.)-504(Since)-349(I)-349(think)-350(it)-349(will)-349(b)-27(e)-350(easier,)-355(let's)-349(fo)-27(cus)-349(on)]TJ/F18 11.9552 Tf 0 -14.446 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(\000)]TJ/F18 11.9552 Tf 11.955 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(.)]TJ ET 1 0 0 1 89.559 570.062 cm EMC /P <> BDC 1 0 0 1 -89.559 -570.062 cm BT /F15 11.9552 Tf 89.559 570.062 Td [(W)82(e)-362(supp)-28(osed)-362(that)]TJ/F18 11.9552 Tf 97.33 0 Td [(x)-339(>)-338(y)]TJ/F15 11.9552 Tf 32.935 0 Td [(+)-246(1.)-543(By)-362(subtracting)]TJ/F18 11.9552 Tf 108.709 0 Td [(y)]TJ/F15 11.9552 Tf 10.466 0 Td [(w)27(e)-362(get)]TJ/F18 11.9552 Tf 37.597 0 Td [(x)]TJ/F21 11.9552 Tf 9.599 0 Td [(\000)]TJ/F18 11.9552 Tf 12.246 0 Td [(y)-374(>)]TJ/F15 11.9552 Tf 23.336 0 Td [(1,)-371(and)-362(w)27(e're)-362(half)-362(done.)]TJ -349.777 -14.446 Td [(W)82(e)-404(also)-403(supp)-28(osed)-403(that)]TJ/F18 11.9552 Tf 123.216 0 Td [(x)-409(>)-409(y)]TJ/F15 11.9552 Tf 31.674 0 Td [(.)-667(By)-403(subtracting)-403(1)-404(w)27(e)-403(also)-404(get)]TJ/F18 11.9552 Tf 166.947 0 Td [(x)]TJ/F21 11.9552 Tf 9.936 0 Td [(\000)]TJ/F15 11.9552 Tf 12.584 0 Td [(1)]TJ/F18 11.9552 Tf 10.743 0 Td [(>)-409(y)]TJ/F21 11.9552 Tf 23.417 0 Td [(\000)]TJ/F15 11.9552 Tf 12.583 0 Td [(1.)-667(Mult)1(iplying)]TJ -391.1 -14.445 Td [(these)-367(t)27(w)27(o)-367(pro)-27(duces)]TJ/F18 11.9552 Tf 102.722 0 Td [(x)]TJ/F16 7.9701 Tf 6.653 4.338 Td [(2)]TJ/F21 11.9552 Tf 7.721 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 12.288 0 Td [(x)-347(>)-348(y)]TJ/F16 7.9701 Tf 30.198 4.338 Td [(2)]TJ/F21 11.9552 Tf 7.722 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 12.288 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(,)-377(and)-368(subtractin)1(g)]TJ/F18 11.9552 Tf 93.35 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 9.123 -4.338 Td [(and)-367(adding)]TJ/F18 11.9552 Tf 62.108 0 Td [(x)]TJ/F15 11.9552 Tf 11.043 0 Td [(to)-367(b)-27(oth)-368(sides)-367(yields)]TJ/F18 11.9552 Tf -367.489 -14.446 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.459 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.024 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F18 11.9552 Tf 8.053 -4.338 Td [(>)-278(x)]TJ/F21 11.9552 Tf 20.804 0 Td [(\000)]TJ/F18 11.9552 Tf 11.025 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(,)-296(as)-288(desired.)-423(W)82(e'v)27(e)-288(no)27(w)-288(sho)27(wn)-288(that)-288(\050)]TJ/F18 11.9552 Tf 187.294 0 Td [(x)]TJ/F21 11.9552 Tf 8.379 0 Td [(\000)]TJ/F18 11.9552 Tf 11.024 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 4.552 0 Td [(j)]TJ/F15 11.9552 Tf 3.321 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.458 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.025 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 4.732 -4.338 Td [(\051)-288(and)-288(1)]TJ/F18 11.9552 Tf 39.479 0 Td [(<)-278(x)]TJ/F21 11.9552 Tf 20.803 0 Td [(\000)]TJ/F18 11.9552 Tf 11.025 0 Td [(y)-314(<)-277(x)]TJ/F16 7.9701 Tf 28.535 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.459 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.024 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 4.732 -4.338 Td [(,)]TJ -464.748 -14.446 Td [(therefore)-326(b)27(y)-326(de\014nition)]TJ/F18 11.9552 Tf 117.385 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 7.389 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.955 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 8.634 -4.338 Td [(is)-326(comp)-27(osite,)-327(as)-326(claimed.)]TJ ET 1 0 0 1 89.559 485.878 cm EMC /P <> BDC 1 0 0 1 -89.559 -485.878 cm BT /F15 11.9552 Tf 89.559 485.878 Td [(5.23.)-427(Sup)1(p)-28(ose)-300(y)27(ou)-301(are)-301(ask)27(ed)-300(to)-301(pro)27(v)27(e)-300(a)-301(statemen)27(t)-301(of)-300(the)-301(form)-301(If)-301(A)-301(o)1(r)-301(B,)-301(then)-301(C.)-301(Exp)1(lain)]TJ -17.559 -14.446 Td [(wh)27(y)-264(y)28(ou)-264(need)-264(to)-264(pro)28(v)27(e)-264(\050a\051)-264(If)-264(A,)-264(then)-263(C.)-264(and)-264(also)-264(pro)27(v)28(e)-264(\050b\051)-264(If)-264(B,)-264(then)-263(C.)-264(Wh)27(y)-264(is)-264(it)-264(n)1(ot)-264(enough)]TJ 0 -14.446 Td [(to)-326(pro)27(v)27(e)-326(only)-327(o)1(ne)-327(of)-326(\050a\051)-327(o)1(r)-327(\050b\051?)]TJ ET 1 0 0 1 89.559 442.54 cm EMC /P <> BDC 1 0 0 1 -89.559 -442.54 cm BT /F15 11.9552 Tf 89.559 442.54 Td [(Consider)-372(the)-372(statemen)27(t)-372(If)-372(I)-372(am)-372(aliv)28(e)-373(o)1(r)-373(de)1(ad,)-384(then)-372(I)-372(am)-372(aliv)27(e.)-372(W)82(ell,)-383(it)-372(is)-373(tru)1(e)-373(th)1(at)-373(If)-372(I)]TJ -17.559 -14.445 Td [(am)-325(aliv)27(e,)-325(then)-325(I)-325(am)-324(aliv)27(e,)-325(trivially)82(.)-435(Ho)27(w)27(ev)28(er,)-325(the)-325(original)-325(statemen)27(t)-325(is)-325(not)-325(t)1(rue.)-435(This)-325(sho)27(ws)]TJ 0 -14.446 Td [(that)-297(it)-297(is)-298(not)-297(enough)-297(to)-297(pro)27(v)27(e)-297(only)-297(one,)-303(but)-297(not)-297(quite)-298(wh)28(y)81(.)-425(T)81(o)-297(see)-297(wh)27(y)82(,)-303(examine)-297(the)-298(o)1(riginal)]TJ 0 -14.446 Td [(statemen)27(t)-380(If)-380(A)-380(or)-380(B,)-380(then)-380(C.)-380(This)-380(sa)27(ys)-380(that)-380(if)-380(one)-380(of)-380(A)-380(or)-380(B)-380(is)-380(true,)-394(C)-380(m)28(ust)-380(also)-380(b)-28(e)-380(true)]TJ 0 -14.446 Td [(as)-348(w)27(ell.)-500(In)-347(either)-348(the)-348(case)-348(that)-348(A)-348(is)-348(true)-348(or)-348(that)-348(B)-347(is)-348(true,)-354(C)-348(m)28(ust)-348(follo)27(w)-348(to)-348(b)-27(e)-348(true.)-500(If)-348(w)28(e)]TJ 0 -14.446 Td [(only)-342(c)27(hec)27(k)-342(the)-343(A)-342(is)-343(true)-342(case,)-347(w)27(e)-342(ha)27(v)27(e)-342(not)-342(attended)-343(to)-342(the)-343(B)-342(is)-343(true)-342(case.)-484(Thi)1(s)-343(case)-342(is)-343(also)]TJ 0 -14.445 Td [(necessary)-326(for)-327(pro)28(ving)-327(the)-326(statemen)27(t)-326(If)-326(A)-327(or)-326(B,)-327(t)1(hen)-327(C.)]TJ ET 1 0 0 1 89.559 329.465 cm EMC /P <> BDC 1 0 0 1 -89.559 -329.465 cm BT /F15 11.9552 Tf 89.559 329.465 Td [(6.2.)-435(Dispro)27(v)27(e:)-435(If)]TJ/F18 11.9552 Tf 88.016 0 Td [(a)]TJ/F15 11.9552 Tf 10.047 0 Td [(and)]TJ/F18 11.9552 Tf 22.762 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(are)-326(nonnegativ)27(e)-326(in)27(tegers)-326(with)]TJ/F18 11.9552 Tf 154.519 0 Td [(a)]TJ/F21 11.9552 Tf 9.466 0 Td [(j)]TJ/F18 11.9552 Tf 6.641 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(,)-326(then)]TJ/F18 11.9552 Tf 33.818 0 Td [(a)]TJ/F21 11.9552 Tf 9.465 0 Td [(\024)]TJ/F18 11.9552 Tf 12.62 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(.)]TJ ET 1 0 0 1 89.559 315.019 cm EMC /P <> BDC 1 0 0 1 -89.559 -315.019 cm BT /F15 11.9552 Tf 89.559 315.019 Td [(2)-326(and)-327(0)-326(are)-326(nonnegativ)27(e)-326(in)27(tegers,)-326(2)]TJ/F21 11.9552 Tf 182.552 0 Td [(j)]TJ/F15 11.9552 Tf 6.642 0 Td [(0)-326(\050b)-28(ec)1(ause)-327(0)-278(=)-277(2)]TJ/F21 11.9552 Tf 87.728 0 Td [(\002)]TJ/F15 11.9552 Tf 11.956 0 Td [(0\051,)-326(but)-327(it)-326(is)-326(false)-327(that)-326(2)]TJ/F21 11.9552 Tf 123.437 0 Td [(\024)]TJ/F15 11.9552 Tf 12.619 0 Td [(0.)]TJ ET 1 0 0 1 89.559 288.618 cm EMC /P <> BDC 1 0 0 1 -89.559 -288.618 cm BT /F15 11.9552 Tf 89.559 288.618 Td [(6.4)-343(Exp)-27(onen)27(tiation)-343(\050or)-344(in)28(v)27(olution\051)-343(is)-344(not)-343(asso)-27(ciativ)27(e.)-486(Those)-343(paren)27(thesis)-343(matter.)-486(2)]TJ/F16 7.9701 Tf 422.201 4.338 Td [(\0503)]TJ/F17 5.9776 Tf 7.527 2.813 Td [(2)]TJ/F16 7.9701 Tf 4.151 -2.813 Td [(\051)]TJ/F15 11.9552 Tf 7.457 -4.338 Td [(=)]TJ -458.895 -14.446 Td [(2)]TJ/F16 7.9701 Tf 5.853 4.338 Td [(9)]TJ/F15 11.9552 Tf 9.773 -4.338 Td [(=)-422(51)1(2,)-432(while)-411(\0502)]TJ/F16 7.9701 Tf 82.101 4.338 Td [(3)]TJ/F15 11.9552 Tf 4.732 -4.338 Td [(\051)]TJ/F16 7.9701 Tf 4.553 4.338 Td [(2)]TJ/F15 11.9552 Tf 9.772 -4.338 Td [(=)-422(8)]TJ/F16 7.9701 Tf 19.998 4.338 Td [(2)]TJ/F15 11.9552 Tf 9.773 -4.338 Td [(=)-422(64)1(.)-689(These)-411(are)-411(all)-411(p)-27(ositiv)27(e)-410(in)27(tegers,)-432(but)-411(the)-411(results)-411(a)1(re)-411(not)]TJ -146.555 -14.446 Td [(equal.)]TJ ET 1 0 0 1 89.559 233.325 cm EMC /P <> BDC 1 0 0 1 -89.559 -233.325 cm BT /F15 11.9552 Tf 89.559 233.325 Td [([extra])-421(6.7)-420(This)-421(isn't)-421(to)-27(o)-421(bad)-420(for)-421(y)27(our)-421(calculator)-420(to)-421(handle.)-718(2)]TJ/F16 7.9701 Tf 327.286 4.338 Td [(2)]TJ/F17 5.9776 Tf 4.234 2.813 Td [(5)]TJ/F15 11.9552 Tf 8.074 -7.151 Td [(+)-286(1)-439(=)-438(4294967297)-439(=)]TJ -357.153 -14.446 Td [(641\0506700417\051.)-595(Clearly)-379(1)]TJ/F18 11.9552 Tf 129.539 0 Td [(<)]TJ/F15 11.9552 Tf 13.509 0 Td [(641)]TJ/F18 11.9552 Tf 21.964 0 Td [(<)]TJ/F15 11.9552 Tf 13.509 0 Td [(4294967297,)-393(and)-379(so)-380(2)]TJ/F16 7.9701 Tf 110.74 4.339 Td [(2)]TJ/F20 5.9776 Tf 4.234 2.812 Td [(n)]TJ/F15 11.9552 Tf 8.687 -7.151 Td [(+)-258(1)-380(is)-380(not)-379(prime)-380(for)]TJ/F18 11.9552 Tf 108.766 0 Td [(n)]TJ/F15 11.9552 Tf 11.392 0 Td [(=)-368(5.)-595([Of)]TJ -422.34 -14.446 Td [(historical)-371(note:)-524(Pierre)-371(de)-370(F)81(ermat)-371(thou)1(gh)27(t)-371(all)-371(n)27(um)28(b)-28(ers)-370(2)]TJ/F16 7.9701 Tf 290.084 4.339 Td [(2)]TJ/F20 5.9776 Tf 4.234 2.813 Td [(n)]TJ/F15 11.9552 Tf 8.616 -7.152 Td [(+)-252(1)-371(w)27(ere)-371(prime,)-382(mostly)-371(b)-27(ecause)]TJ -302.934 -14.446 Td [(the)-326(n)27(um)27(b)-27(ers)-326(grew)-327(to)-27(o)-326(big)-327(t)1(o)-327(compute.])]TJ ET 1 0 0 1 89.559 163.587 cm EMC /P <> BDC 1 0 0 1 -89.559 -163.587 cm BT /F15 11.9552 Tf 89.559 163.587 Td [([extra])-528(6.)1(9)-528(Consider)]TJ/F18 11.9552 Tf 111.662 0 Td [(n)]TJ/F16 7.9701 Tf 6.988 4.338 Td [(2)]TJ/F15 11.9552 Tf 9.027 -4.338 Td [(+)]TJ/F18 11.9552 Tf 13.4 0 Td [(n)]TJ/F15 11.9552 Tf 11.282 0 Td [(+)-359(41.)-1039(Calculate)-528(the)-527(v)54(alue)-527(of)-528(this)-528(p)-27(olynomial)-527(for)]TJ/F18 11.9552 Tf 274.573 0 Td [(n)]TJ/F15 11.9552 Tf 14.404 0 Td [(=)]TJ -458.895 -14.446 Td [(1)]TJ/F18 11.9552 Tf 5.853 0 Td [(;)]TJ/F15 11.9552 Tf 5.244 0 Td [(2)]TJ/F18 11.9552 Tf 5.853 0 Td [(;)]TJ/F15 11.9552 Tf 5.244 0 Td [(3)]TJ/F18 11.9552 Tf 5.853 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F15 11.9552 Tf 26.221 0 Td [(10.)]TJ ET 1 0 0 1 146.428 149.141 cm EMC 1 0 0 1 -45.163 -24.409 cm /Quote <> BDC 1 0 0 1 -101.265 -124.732 cm BT /F15 11.9552 Tf 101.265 124.732 Td [(43,)-326(47,)-327(53,)-326(61,)-326(71,)-327(83,)-326(97,)-326(113,)-327(131,)-326(151)]TJ ET 1 0 0 1 304.169 124.732 cm EMC 1 0 0 1 -232.169 -24.408 cm /P <> BDC 1 0 0 1 -72 -100.324 cm BT /F15 11.9552 Tf 72 100.324 Td [(Notice)-326(that)-327(all)-326(the)-326(n)27(um)27(b)-27(ers)-326(y)27(ou)-326(computed)-327(are)-326(prime)-326(\050y)27(ep)-326(they)-327(are\051.)]TJ ET 1 0 0 1 427.467 100.324 cm EMC 1 0 0 1 -326.202 -24.409 cm /Quote <> BDC 1 0 0 1 -101.265 -75.915 cm BT /F15 11.9552 Tf 101.265 75.915 Td [(Dispro)27(v)27(e)1(:)-436(If)]TJ/F18 11.9552 Tf 64.604 0 Td [(n)]TJ/F15 11.9552 Tf 10.89 0 Td [(is)-326(a)-327(p)-27(ositiv)27(e)-326(in)27(teger,)-326(then)]TJ/F18 11.9552 Tf 133.448 0 Td [(n)]TJ/F16 7.9701 Tf 6.988 4.339 Td [(2)]TJ/F15 11.9552 Tf 7.389 -4.339 Td [(+)]TJ/F18 11.9552 Tf 11.761 0 Td [(n)]TJ/F15 11.9552 Tf 9.644 0 Td [(+)-222(41)-327(is)-326(prime.)]TJ ET 1 0 0 1 422.849 75.915 cm EMC 1 0 0 1 -333.29 -24.408 cm /P <> BDC 1 0 0 1 -89.559 -51.507 cm BT /F15 11.9552 Tf 89.559 51.507 Td [(Doing)-269(this)-268(b)27(y)-269(blind)-268(computation)-269(is)-268(incon)27(v)27(enien)28(t)-269(\050turns)-269(out)-268(they)-269(all)-269(a)1(re)-269(for)-269(quite)-268(a)-269(while\051.)]TJ -17.559 -14.446 Td [(But)-312(some)-312(though)28(t)-312(reminds)-312(us)-312(that)-312(clearly)-312(if)]TJ/F18 11.9552 Tf 227.893 0 Td [(n)]TJ/F15 11.9552 Tf 10.309 0 Td [(=)-278(41)-312(then)-312(4)1(1)]TJ/F16 7.9701 Tf 66.058 4.338 Td [(2)]TJ/F15 11.9552 Tf 7.037 -4.338 Td [(+)-193(41)-192(+)-193(41)-312(can't)-312(b)-27(e)-312(prime,)-315(41)-312(is)]TJ ET 1 0 0 1 72 37.061 cm EMC endstream endobj 4 0 obj << /Type /ObjStm /N 100 /First 800 /Length 10980 >> stream 3 0 6 41 7 139 8 237 9 335 10 433 11 538 12 637 13 742 14 841 15 940 16 1039 17 1139 18 1239 5 1339 22 1441 23 1486 20 1535 19 1672 33 1807 34 1908 35 2015 36 2116 37 2217 38 2318 39 2419 40 2520 41 2627 42 2728 43 2829 44 2930 45 3031 46 3132 47 3233 48 3334 49 3441 50 3542 51 3643 52 3744 32 3851 57 3954 55 4005 53 4118 58 4219 59 4320 60 4421 61 4522 62 4623 63 4724 64 4825 65 4926 66 5027 67 5134 68 5235 54 5342 72 5445 70 5491 69 5616 75 5752 76 5853 77 5954 78 6055 79 6156 83 6257 84 6362 85 6467 86 6572 87 6677 82 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0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -261.603 -406.527 cm BT /F18 11.9552 Tf 265.505 406.527 Td [(z)]TJ ET 1 0 0 1 275.377 406.527 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -289.325 -406.527 cm BT /F18 11.9552 Tf 293.227 406.527 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)]TJ/F18 11.9552 Tf 10.626 0 Td [(y)]TJ ET 1 0 0 1 323.201 406.527 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -335.156 -406.527 cm BT /F15 11.9552 Tf 339.058 406.527 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)]TJ/F18 11.9552 Tf 10.627 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.873 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ ET 1 0 0 1 398.802 406.527 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -191.582 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 197.56 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -207.22 -401.795 cm BT /F15 11.9552 Tf 214.247 391.683 Td [(T)]TJ ET 1 0 0 1 222.702 391.683 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.748 0 cm /TD <> BDC 1 0 0 1 -238.45 -391.683 cm BT /F15 11.9552 Tf 238.45 391.683 Td [(T)]TJ ET 1 0 0 1 246.904 391.683 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.359 0 cm /TD <> BDC 1 0 0 1 -264.263 -391.683 cm BT /F15 11.9552 Tf 264.263 391.683 Td [(T)]TJ ET 1 0 0 1 272.717 391.683 cm EMC q 1 0 0 1 8.638 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.319 0 cm /TD <> BDC 1 0 0 1 -302.036 -391.683 cm BT /F15 11.9552 Tf 302.036 391.683 Td [(T)]TJ ET 1 0 0 1 310.49 391.683 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.311 0 cm /TD <> BDC 1 0 0 1 -360.801 -391.683 cm BT /F15 11.9552 Tf 360.801 391.683 Td [(T)]TJ ET 1 0 0 1 373.157 391.683 cm EMC /TD <> BDC q 1 0 0 1 31.623 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.937 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -373.157 -391.683 cm BT /F15 11.9552 Tf 214.247 377.237 Td [(T)]TJ ET 1 0 0 1 222.702 377.237 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.748 0 cm /TD <> BDC 1 0 0 1 -238.45 -377.237 cm BT /F15 11.9552 Tf 238.45 377.237 Td [(T)]TJ ET 1 0 0 1 246.904 377.237 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -264.67 -377.237 cm BT /F15 11.9552 Tf 264.67 377.237 Td [(F)]TJ ET 1 0 0 1 272.31 377.237 cm EMC q 1 0 0 1 9.045 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.037 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.726 0 cm /TD <> BDC 1 0 0 1 -302.036 -377.237 cm BT /F15 11.9552 Tf 302.036 377.237 Td [(T)]TJ ET 1 0 0 1 310.49 377.237 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.719 0 cm /TD <> BDC 1 0 0 1 -361.209 -377.237 cm BT /F15 11.9552 Tf 361.209 377.237 Td [(F)]TJ ET 1 0 0 1 372.75 377.237 cm EMC /TD <> BDC q 1 0 0 1 32.03 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.53 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -372.75 -377.237 cm BT /F15 11.9552 Tf 214.247 362.791 Td [(T)]TJ ET 1 0 0 1 222.702 362.791 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.155 0 cm /TD <> BDC 1 0 0 1 -238.857 -362.791 cm BT /F15 11.9552 Tf 238.857 362.791 Td [(F)]TJ ET 1 0 0 1 246.497 362.791 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -264.263 -362.791 cm BT /F15 11.9552 Tf 264.263 362.791 Td [(T)]TJ ET 1 0 0 1 272.717 362.791 cm EMC q 1 0 0 1 8.638 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.319 0 cm /TD <> BDC 1 0 0 1 -302.036 -362.791 cm BT /F15 11.9552 Tf 302.036 362.791 Td [(T)]TJ ET 1 0 0 1 310.49 362.791 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.311 0 cm /TD <> BDC 1 0 0 1 -360.801 -362.791 cm BT /F15 11.9552 Tf 360.801 362.791 Td [(T)]TJ ET 1 0 0 1 373.157 362.791 cm EMC /TD <> BDC q 1 0 0 1 31.623 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.937 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -373.157 -362.791 cm BT /F15 11.9552 Tf 214.247 348.345 Td [(T)]TJ ET 1 0 0 1 222.702 348.345 cm EMC q 1 0 0 1 7.027 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.155 0 cm /TD <> BDC 1 0 0 1 -238.857 -348.345 cm BT /F15 11.9552 Tf 238.857 348.345 Td [(F)]TJ ET 1 0 0 1 246.497 348.345 cm EMC q 1 0 0 1 9.128 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 18.173 0 cm /TD <> BDC 1 0 0 1 -264.67 -348.345 cm BT /F15 11.9552 Tf 264.67 348.345 Td [(F)]TJ ET 1 0 0 1 272.31 348.345 cm EMC q 1 0 0 1 9.045 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.037 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.726 0 cm /TD <> BDC 1 0 0 1 -302.036 -348.345 cm BT /F15 11.9552 Tf 302.036 348.345 Td [(T)]TJ ET 1 0 0 1 310.49 348.345 cm EMC q 1 0 0 1 18.689 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.719 0 cm /TD <> BDC 1 0 0 1 -361.209 -348.345 cm BT /F15 11.9552 Tf 361.209 348.345 Td [(F)]TJ ET 1 0 0 1 372.75 348.345 cm EMC /TD <> BDC q 1 0 0 1 32.03 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.53 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -372.75 -348.345 cm BT /F15 11.9552 Tf 214.655 333.9 Td [(F)]TJ ET 1 0 0 1 222.294 333.9 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.156 0 cm /TD <> BDC 1 0 0 1 -238.45 -333.9 cm BT /F15 11.9552 Tf 238.45 333.9 Td [(T)]TJ ET 1 0 0 1 246.904 333.9 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.359 0 cm /TD <> BDC 1 0 0 1 -264.263 -333.9 cm BT /F15 11.9552 Tf 264.263 333.9 Td [(T)]TJ ET 1 0 0 1 272.717 333.9 cm EMC q 1 0 0 1 8.638 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.319 0 cm /TD <> BDC 1 0 0 1 -302.036 -333.9 cm BT /F15 11.9552 Tf 302.036 333.9 Td [(T)]TJ ET 1 0 0 1 310.49 333.9 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.311 0 cm /TD <> BDC 1 0 0 1 -360.801 -333.9 cm BT /F15 11.9552 Tf 360.801 333.9 Td [(T)]TJ ET 1 0 0 1 373.157 333.9 cm EMC /TD <> BDC q 1 0 0 1 31.623 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.937 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -373.157 -333.9 cm BT /F15 11.9552 Tf 214.655 319.454 Td [(F)]TJ ET 1 0 0 1 222.294 319.454 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.156 0 cm /TD <> BDC 1 0 0 1 -238.45 -319.454 cm BT /F15 11.9552 Tf 238.45 319.454 Td [(T)]TJ ET 1 0 0 1 246.904 319.454 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -264.67 -319.454 cm BT /F15 11.9552 Tf 264.67 319.454 Td [(F)]TJ ET 1 0 0 1 272.309 319.454 cm EMC q 1 0 0 1 9.046 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.038 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.727 0 cm /TD <> BDC 1 0 0 1 -302.036 -319.454 cm BT /F15 11.9552 Tf 302.036 319.454 Td [(T)]TJ ET 1 0 0 1 310.49 319.454 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.719 0 cm /TD <> BDC 1 0 0 1 -361.209 -319.454 cm BT /F15 11.9552 Tf 361.209 319.454 Td [(F)]TJ ET 1 0 0 1 372.75 319.454 cm EMC /TD <> BDC q 1 0 0 1 32.03 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.53 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -372.75 -319.454 cm BT /F15 11.9552 Tf 214.655 305.008 Td [(F)]TJ ET 1 0 0 1 222.294 305.008 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.563 0 cm /TD <> BDC 1 0 0 1 -238.857 -305.008 cm BT /F15 11.9552 Tf 238.857 305.008 Td [(F)]TJ ET 1 0 0 1 246.497 305.008 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -264.263 -305.008 cm BT /F15 11.9552 Tf 264.263 305.008 Td [(T)]TJ ET 1 0 0 1 272.717 305.008 cm EMC q 1 0 0 1 8.638 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.726 0 cm /TD <> BDC 1 0 0 1 -302.443 -305.008 cm BT /F15 11.9552 Tf 302.443 305.008 Td [(F)]TJ ET 1 0 0 1 310.083 305.008 cm EMC q 1 0 0 1 19.096 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 52.669 0 cm /TD <> BDC 1 0 0 1 -362.752 -305.008 cm BT /F15 11.9552 Tf 362.752 305.008 Td [(T)]TJ ET 1 0 0 1 371.206 305.008 cm EMC /TD <> BDC q 1 0 0 1 33.574 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -163.986 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -371.206 -305.008 cm BT /F15 11.9552 Tf 214.655 290.562 Td [(F)]TJ ET 1 0 0 1 222.294 290.562 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.563 0 cm /TD <> BDC 1 0 0 1 -238.857 -290.562 cm BT /F15 11.9552 Tf 238.857 290.562 Td [(F)]TJ ET 1 0 0 1 246.497 290.562 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 18.173 0 cm /TD <> BDC 1 0 0 1 -264.67 -290.562 cm BT /F15 11.9552 Tf 264.67 290.562 Td [(F)]TJ ET 1 0 0 1 272.31 290.562 cm EMC q 1 0 0 1 9.045 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.037 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.133 0 cm /TD <> BDC 1 0 0 1 -302.443 -290.562 cm BT /F15 11.9552 Tf 302.443 290.562 Td [(F)]TJ ET 1 0 0 1 310.083 290.562 cm EMC q 1 0 0 1 19.096 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 52.669 0 cm /TD <> BDC 1 0 0 1 -362.752 -290.562 cm BT /F15 11.9552 Tf 362.752 290.562 Td [(T)]TJ ET 1 0 0 1 371.206 290.562 cm EMC /TD <> BDC q 1 0 0 1 33.574 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -163.986 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 197.56 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.509 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 197.56 55.392 cm EMC 1 0 0 1 -332.78 -76.652 cm /TD <> BDC 1 0 0 1 91.628 -0.996 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 284.743 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -163.628 -263.175 cm BT /F18 11.9552 Tf 170.507 253.063 Td [(x)]TJ ET 1 0 0 1 177.159 253.063 cm EMC q 1 0 0 1 6.879 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.856 0 cm /TD <> BDC 1 0 0 1 -190.015 -253.063 cm BT /F18 11.9552 Tf 193.917 253.063 Td [(y)]TJ ET 1 0 0 1 203.956 253.063 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -215.911 -253.063 cm BT /F18 11.9552 Tf 219.813 253.063 Td [(z)]TJ ET 1 0 0 1 229.686 253.063 cm EMC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -243.634 -253.063 cm BT /F18 11.9552 Tf 247.536 253.063 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ ET 1 0 0 1 282.657 253.063 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -294.612 -253.063 cm BT /F18 11.9552 Tf 298.514 253.063 Td [(y)]TJ/F21 11.9552 Tf 9.458 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ ET 1 0 0 1 333.12 253.063 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -345.076 -253.063 cm BT /F15 11.9552 Tf 348.978 253.063 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.97 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(y)]TJ/F21 11.9552 Tf 9.457 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.971 0 Td [(\051)]TJ ET 1 0 0 1 442.394 253.063 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -278.766 -4.333 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 284.743 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -163.628 -248.331 cm BT /F15 11.9552 Tf 169.606 238.219 Td [(T)]TJ ET 1 0 0 1 178.06 238.219 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.699 0 cm /TD <> BDC 1 0 0 1 -192.759 -238.219 cm BT /F15 11.9552 Tf 192.759 238.219 Td [(T)]TJ ET 1 0 0 1 201.213 238.219 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.358 0 cm /TD <> BDC 1 0 0 1 -218.571 -238.219 cm BT /F15 11.9552 Tf 218.571 238.219 Td [(T)]TJ ET 1 0 0 1 227.026 238.219 cm EMC q 1 0 0 1 8.637 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 31.892 0 cm /TD <> BDC 1 0 0 1 -258.918 -238.219 cm BT /F15 11.9552 Tf 258.918 238.219 Td [(T)]TJ ET 1 0 0 1 267.373 238.219 cm EMC q 1 0 0 1 21.262 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.266 0 cm /TD <> BDC 1 0 0 1 -309.639 -238.219 cm BT /F15 11.9552 Tf 309.639 238.219 Td [(T)]TJ ET 1 0 0 1 318.093 238.219 cm EMC q 1 0 0 1 21.005 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 71.415 0 cm /TD <> BDC 1 0 0 1 -389.508 -238.219 cm BT /F15 11.9552 Tf 389.508 238.219 Td [(T)]TJ ET 1 0 0 1 397.962 238.219 cm EMC /TD <> BDC q 1 0 0 1 50.41 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -234.334 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -397.962 -238.219 cm BT /F15 11.9552 Tf 169.606 223.773 Td [(T)]TJ ET 1 0 0 1 178.06 223.773 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.699 0 cm /TD <> BDC 1 0 0 1 -192.759 -223.773 cm BT /F15 11.9552 Tf 192.759 223.773 Td [(T)]TJ ET 1 0 0 1 201.213 223.773 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -218.979 -223.773 cm BT /F15 11.9552 Tf 218.979 223.773 Td [(F)]TJ ET 1 0 0 1 226.618 223.773 cm EMC q 1 0 0 1 9.045 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.038 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.708 0 cm /TD <> BDC 1 0 0 1 -259.326 -223.773 cm BT /F15 11.9552 Tf 259.326 223.773 Td [(F)]TJ ET 1 0 0 1 266.965 223.773 cm EMC q 1 0 0 1 21.67 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 43.082 0 cm /TD <> BDC 1 0 0 1 -310.047 -223.773 cm BT /F15 11.9552 Tf 310.047 223.773 Td [(F)]TJ ET 1 0 0 1 317.686 223.773 cm EMC q 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cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.873 0 cm /TD <> BDC 1 0 0 1 -232.226 -526.629 cm BT /F15 11.9552 Tf 232.226 526.629 Td [(F)]TJ ET 1 0 0 1 239.865 526.629 cm EMC q 1 0 0 1 21.753 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 58.026 0 cm /TD <> BDC 1 0 0 1 -297.891 -526.629 cm BT /F15 11.9552 Tf 297.891 526.629 Td [(F)]TJ ET 1 0 0 1 305.53 526.629 cm EMC q 1 0 0 1 36.273 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 87.106 0 cm /TD <> BDC 1 0 0 1 -392.636 -526.629 cm BT /F15 11.9552 Tf 392.636 526.629 Td [(T)]TJ ET 1 0 0 1 401.091 526.629 cm EMC /TD <> BDC q 1 0 0 1 50.833 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -241.015 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -401.091 -526.629 cm BT /F15 11.9552 Tf 167.511 512.183 Td [(F)]TJ ET 1 0 0 1 175.15 512.183 cm EMC q 1 0 0 1 7.435 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.156 0 cm /TD <> BDC 1 0 0 1 -191.306 -512.183 cm BT /F15 11.9552 Tf 191.306 512.183 Td [(T)]TJ ET 1 0 0 1 199.76 512.183 cm EMC q 1 0 0 1 8.721 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.713 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.059 0 cm /TD <> BDC 1 0 0 1 -231.819 -512.183 cm BT /F15 11.9552 Tf 231.819 512.183 Td [(T)]TJ ET 1 0 0 1 240.273 512.183 cm EMC q 1 0 0 1 21.345 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 57.618 0 cm /TD <> BDC 1 0 0 1 -297.891 -512.183 cm BT /F15 11.9552 Tf 297.891 512.183 Td [(F)]TJ ET 1 0 0 1 305.53 512.183 cm EMC q 1 0 0 1 36.273 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 87.106 0 cm /TD <> BDC 1 0 0 1 -392.636 -512.183 cm BT /F15 11.9552 Tf 392.636 512.183 Td [(T)]TJ ET 1 0 0 1 401.091 512.183 cm EMC /TD <> BDC q 1 0 0 1 50.833 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -241.015 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -401.091 -512.183 cm BT /F15 11.9552 Tf 167.511 497.738 Td [(F)]TJ ET 1 0 0 1 175.15 497.738 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.563 0 cm /TD <> BDC 1 0 0 1 -191.713 -497.738 cm BT /F15 11.9552 Tf 191.713 497.738 Td [(F)]TJ ET 1 0 0 1 199.353 497.738 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.12 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.466 0 cm /TD <> BDC 1 0 0 1 -231.819 -497.738 cm BT /F15 11.9552 Tf 231.819 497.738 Td [(T)]TJ ET 1 0 0 1 240.273 497.738 cm EMC q 1 0 0 1 21.345 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 57.618 0 cm /TD <> BDC 1 0 0 1 -297.891 -497.738 cm BT /F15 11.9552 Tf 297.891 497.738 Td [(F)]TJ ET 1 0 0 1 305.53 497.738 cm EMC q 1 0 0 1 36.273 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 87.106 0 cm /TD <> BDC 1 0 0 1 -392.636 -497.738 cm BT /F15 11.9552 Tf 392.636 497.738 Td [(T)]TJ ET 1 0 0 1 401.091 497.738 cm EMC /TD <> BDC q 1 0 0 1 50.833 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -241.015 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 291.848 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.509 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 291.848 26.501 cm EMC 1 0 0 1 -362.365 -58.354 cm /P <> BDC 1 0 0 1 -89.559 -461.152 cm BT /F15 11.9552 Tf 89.559 461.152 Td [(\050c\051)-326(\050)]TJ/F21 11.9552 Tf 22.762 0 Td [(:)]TJ/F15 11.9552 Tf 7.97 0 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.426 0 Td [($)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 72 450.718 cm EMC /TD <> BDC 1 0 0 1 146.73 -0.996 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 174.539 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -218.73 -449.323 cm BT /F18 11.9552 Tf 225.609 439.211 Td [(x)]TJ ET 1 0 0 1 232.261 439.211 cm EMC q 1 0 0 1 6.879 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.871 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.849 0 cm /TD <> BDC 1 0 0 1 -247.11 -439.211 cm BT /F21 11.9552 Tf 247.11 439.211 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ ET 1 0 0 1 261.732 439.211 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -273.687 -439.211 cm BT /F21 11.9552 Tf 273.687 439.211 Td [(:)]TJ/F15 11.9552 Tf 7.97 0 Td [(\050)]TJ/F21 11.9552 Tf 4.553 0 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(\051)]TJ ET 1 0 0 1 305.384 439.211 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -317.339 -439.211 cm BT /F15 11.9552 Tf 317.339 439.211 Td [(\050)]TJ/F21 11.9552 Tf 4.553 0 Td [(:)]TJ/F15 11.9552 Tf 7.97 0 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.426 0 Td [($)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 387.292 439.211 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -168.562 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 174.539 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -218.73 -434.479 cm BT /F15 11.9552 Tf 224.708 424.367 Td [(T)]TJ ET 1 0 0 1 233.162 424.367 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.439 0 cm /TD <> BDC 1 0 0 1 -250.601 -424.367 cm BT /F15 11.9552 Tf 250.601 424.367 Td [(F)]TJ ET 1 0 0 1 258.241 424.367 cm EMC q 1 0 0 1 9.469 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 27.068 0 cm /TD <> BDC 1 0 0 1 -285.309 -424.367 cm BT /F15 11.9552 Tf 285.309 424.367 Td [(T)]TJ ET 1 0 0 1 293.763 424.367 cm EMC q 1 0 0 1 17.599 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 54.326 0 cm /TD <> BDC 1 0 0 1 -348.089 -424.367 cm BT /F15 11.9552 Tf 348.089 424.367 Td [(T)]TJ ET 1 0 0 1 356.543 424.367 cm EMC /TD <> BDC q 1 0 0 1 36.727 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -137.813 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -356.543 -424.367 cm BT /F15 11.9552 Tf 225.115 409.921 Td [(F)]TJ ET 1 0 0 1 232.755 409.921 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.377 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.439 0 cm /TD <> BDC 1 0 0 1 -250.194 -409.921 cm BT /F15 11.9552 Tf 250.194 409.921 Td [(T)]TJ ET 1 0 0 1 258.648 409.921 cm EMC q 1 0 0 1 9.062 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 27.068 0 cm /TD <> BDC 1 0 0 1 -285.716 -409.921 cm BT /F15 11.9552 Tf 285.716 409.921 Td [(F)]TJ ET 1 0 0 1 293.355 409.921 cm EMC q 1 0 0 1 18.007 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 54.734 0 cm /TD <> BDC 1 0 0 1 -348.089 -409.921 cm BT /F15 11.9552 Tf 348.089 409.921 Td [(T)]TJ ET 1 0 0 1 356.543 409.921 cm EMC /TD <> BDC q 1 0 0 1 36.727 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -137.813 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 174.539 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 20.41 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.402 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 174.54 12.054 cm EMC 1 0 0 1 -303.711 -43.908 cm /P <> BDC 1 0 0 1 -89.559 -373.335 cm BT /F15 11.9552 Tf 89.559 373.335 Td [(\050d\051)]TJ/F18 11.9552 Tf 19.51 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 72 362.901 cm EMC /TD <> BDC 1 0 0 1 198.92 -0.996 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 70.16 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -270.92 -361.506 cm BT /F18 11.9552 Tf 277.799 351.394 Td [(x)]TJ ET 1 0 0 1 284.451 351.394 cm EMC q 1 0 0 1 6.878 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.871 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.849 0 cm /TD <> BDC 1 0 0 1 -299.3 -351.394 cm BT /F18 11.9552 Tf 299.3 351.394 Td [(x)]TJ/F21 11.9552 Tf 9.972 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 335.103 351.394 cm EMC /TD <> BDC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -64.183 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 70.16 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -270.92 -346.662 cm BT /F15 11.9552 Tf 276.897 336.55 Td [(T)]TJ ET 1 0 0 1 285.352 336.55 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 27.622 0 cm /TD <> BDC 1 0 0 1 -312.974 -336.55 cm BT /F15 11.9552 Tf 312.974 336.55 Td [(T)]TJ ET 1 0 0 1 321.428 336.55 cm EMC /TD <> BDC q 1 0 0 1 19.652 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -50.508 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -321.428 -336.55 cm BT /F15 11.9552 Tf 277.305 322.104 Td [(F)]TJ ET 1 0 0 1 284.944 322.104 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.378 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 28.03 0 cm /TD <> BDC 1 0 0 1 -312.974 -322.104 cm BT /F15 11.9552 Tf 312.974 322.104 Td [(T)]TJ ET 1 0 0 1 321.428 322.104 cm EMC /TD <> BDC q 1 0 0 1 19.652 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -50.508 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 70.16 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 20.409 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.402 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 70.16 12.055 cm EMC 1 0 0 1 -251.521 -43.909 cm /P <> BDC 1 0 0 1 -89.559 -285.518 cm BT /F15 11.9552 Tf 89.559 285.518 Td [(\050e\051)-326(\050\050)]TJ/F18 11.9552 Tf 27.314 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.626 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(y)]TJ/F21 11.9552 Tf 9.457 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.971 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.425 0 Td [(!)]TJ/F15 11.9552 Tf 15.276 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.97 0 Td [(\051)]TJ ET 1 0 0 1 72 275.084 cm EMC /TD <> BDC 1 0 0 1 0 -12.453 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 471.497 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -72 -262.233 cm BT /F18 11.9552 Tf 78.879 252.12 Td [(x)]TJ ET 1 0 0 1 85.531 252.12 cm EMC q 1 0 0 1 6.878 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.015 0 cm /TD <> BDC 1 0 0 1 -99.546 -252.12 cm BT /F18 11.9552 Tf 99.546 252.12 Td [(y)]TJ ET 1 0 0 1 105.683 252.12 cm EMC q 1 0 0 1 7.136 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.355 0 cm /TD <> BDC 1 0 0 1 -120.038 -252.12 cm BT /F18 11.9552 Tf 120.038 252.12 Td [(z)]TJ ET 1 0 0 1 126.009 252.12 cm EMC q 1 0 0 1 7.219 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 9.212 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.19 0 cm /TD <> BDC 1 0 0 1 -141.199 -252.12 cm BT /F18 11.9552 Tf 141.199 252.12 Td [(x)]TJ/F21 11.9552 Tf 9.972 0 Td [(!)]TJ/F18 11.9552 Tf 15.277 0 Td [(y)]TJ ET 1 0 0 1 172.584 252.12 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -184.539 -252.12 cm BT /F18 11.9552 Tf 184.539 252.12 Td [(y)]TJ/F21 11.9552 Tf 9.458 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ ET 1 0 0 1 215.243 252.12 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -227.199 -252.12 cm BT /F15 11.9552 Tf 227.199 252.12 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.626 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(y)]TJ/F21 11.9552 Tf 9.457 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.971 0 Td [(\051)]TJ ET 1 0 0 1 320.781 252.12 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -332.736 -252.12 cm BT /F18 11.9552 Tf 332.736 252.12 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ ET 1 0 0 1 363.956 252.12 cm EMC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -375.911 -252.12 cm BT /F15 11.9552 Tf 375.911 252.12 Td [(\050\050)]TJ/F18 11.9552 Tf 9.105 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(y)]TJ/F21 11.9552 Tf 9.458 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.97 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.426 0 Td [(!)]TJ/F15 11.9552 Tf 15.276 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.971 0 Td [(\051)]TJ ET 1 0 0 1 537.519 252.12 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -465.519 -4.333 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 471.497 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -72 -247.388 cm BT /F15 11.9552 Tf 77.978 237.276 Td [(T)]TJ ET 1 0 0 1 86.432 237.276 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -98.387 -237.276 cm BT /F15 11.9552 Tf 98.387 237.276 Td [(T)]TJ ET 1 0 0 1 106.841 237.276 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -118.797 -237.276 cm BT /F15 11.9552 Tf 118.797 237.276 Td [(T)]TJ ET 1 0 0 1 127.251 237.276 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.413 0 cm /TD <> BDC 1 0 0 1 -152.664 -237.276 cm BT /F15 11.9552 Tf 152.664 237.276 Td [(T)]TJ ET 1 0 0 1 161.119 237.276 cm EMC q 1 0 0 1 17.443 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.545 0 cm /TD <> BDC 1 0 0 1 -195.664 -237.276 cm BT /F15 11.9552 Tf 195.664 237.276 Td [(T)]TJ ET 1 0 0 1 204.119 237.276 cm EMC q 1 0 0 1 17.102 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.644 0 cm /TD <> BDC 1 0 0 1 -269.763 -237.276 cm BT /F15 11.9552 Tf 269.763 237.276 Td [(T)]TJ ET 1 0 0 1 278.217 237.276 cm EMC q 1 0 0 1 48.542 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.902 0 cm /TD <> BDC 1 0 0 1 -344.119 -237.276 cm BT /F15 11.9552 Tf 344.119 237.276 Td [(T)]TJ ET 1 0 0 1 352.573 237.276 cm EMC q 1 0 0 1 17.36 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -237.276 cm BT /F15 11.9552 Tf 452.488 237.276 Td [(T)]TJ ET 1 0 0 1 460.942 237.276 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -237.276 cm BT /F15 11.9552 Tf 77.978 222.83 Td [(T)]TJ ET 1 0 0 1 86.432 222.83 cm EMC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -98.387 -222.83 cm BT /F15 11.9552 Tf 98.387 222.83 Td [(T)]TJ ET 1 0 0 1 106.841 222.83 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -119.204 -222.83 cm BT /F15 11.9552 Tf 119.204 222.83 Td [(F)]TJ ET 1 0 0 1 126.843 222.83 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.378 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.821 0 cm /TD <> BDC 1 0 0 1 -152.664 -222.83 cm BT /F15 11.9552 Tf 152.664 222.83 Td [(T)]TJ ET 1 0 0 1 161.119 222.83 cm EMC q 1 0 0 1 17.443 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.953 0 cm /TD <> BDC 1 0 0 1 -196.072 -222.83 cm BT /F15 11.9552 Tf 196.072 222.83 Td [(F)]TJ ET 1 0 0 1 203.711 222.83 cm EMC q 1 0 0 1 17.51 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.459 0 cm /TD <> BDC 1 0 0 1 -270.17 -222.83 cm BT /F15 11.9552 Tf 270.17 222.83 Td [(F)]TJ ET 1 0 0 1 277.809 222.83 cm EMC q 1 0 0 1 48.95 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.717 0 cm /TD <> BDC 1 0 0 1 -344.526 -222.83 cm BT /F15 11.9552 Tf 344.526 222.83 Td [(F)]TJ ET 1 0 0 1 352.166 222.83 cm EMC q 1 0 0 1 17.767 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 100.322 0 cm /TD <> BDC 1 0 0 1 -452.488 -222.83 cm BT /F15 11.9552 Tf 452.488 222.83 Td [(T)]TJ ET 1 0 0 1 460.942 222.83 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -222.83 cm BT /F15 11.9552 Tf 77.978 208.385 Td [(T)]TJ ET 1 0 0 1 86.432 208.385 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -98.795 -208.385 cm BT /F15 11.9552 Tf 98.795 208.385 Td [(F)]TJ ET 1 0 0 1 106.434 208.385 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -118.797 -208.385 cm BT /F15 11.9552 Tf 118.797 208.385 Td [(T)]TJ ET 1 0 0 1 127.251 208.385 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.821 0 cm /TD <> BDC 1 0 0 1 -153.072 -208.385 cm BT /F15 11.9552 Tf 153.072 208.385 Td [(F)]TJ ET 1 0 0 1 160.711 208.385 cm EMC q 1 0 0 1 17.851 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.953 0 cm /TD <> BDC 1 0 0 1 -195.664 -208.385 cm BT /F15 11.9552 Tf 195.664 208.385 Td [(T)]TJ ET 1 0 0 1 204.119 208.385 cm EMC q 1 0 0 1 17.102 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.051 0 cm /TD <> BDC 1 0 0 1 -270.17 -208.385 cm BT /F15 11.9552 Tf 270.17 208.385 Td [(F)]TJ ET 1 0 0 1 277.809 208.385 cm EMC q 1 0 0 1 48.95 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.31 0 cm /TD <> BDC 1 0 0 1 -344.119 -208.385 cm BT /F15 11.9552 Tf 344.119 208.385 Td [(T)]TJ ET 1 0 0 1 352.573 208.385 cm EMC q 1 0 0 1 17.36 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -208.385 cm BT /F15 11.9552 Tf 452.488 208.385 Td [(T)]TJ ET 1 0 0 1 460.942 208.385 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -208.385 cm BT /F15 11.9552 Tf 77.978 193.939 Td [(T)]TJ ET 1 0 0 1 86.432 193.939 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -98.795 -193.939 cm BT /F15 11.9552 Tf 98.795 193.939 Td [(F)]TJ ET 1 0 0 1 106.434 193.939 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.77 0 cm /TD <> BDC 1 0 0 1 -119.204 -193.939 cm BT /F15 11.9552 Tf 119.204 193.939 Td [(F)]TJ ET 1 0 0 1 126.843 193.939 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.378 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 26.229 0 cm /TD <> BDC 1 0 0 1 -153.072 -193.939 cm BT /F15 11.9552 Tf 153.072 193.939 Td [(F)]TJ ET 1 0 0 1 160.711 193.939 cm EMC q 1 0 0 1 17.851 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.953 0 cm /TD <> BDC 1 0 0 1 -195.664 -193.939 cm BT /F15 11.9552 Tf 195.664 193.939 Td [(T)]TJ ET 1 0 0 1 204.119 193.939 cm EMC q 1 0 0 1 17.102 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.051 0 cm /TD <> BDC 1 0 0 1 -270.17 -193.939 cm BT /F15 11.9552 Tf 270.17 193.939 Td [(F)]TJ ET 1 0 0 1 277.809 193.939 cm EMC q 1 0 0 1 48.95 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.717 0 cm /TD <> BDC 1 0 0 1 -344.526 -193.939 cm BT /F15 11.9552 Tf 344.526 193.939 Td [(F)]TJ ET 1 0 0 1 352.166 193.939 cm EMC q 1 0 0 1 17.767 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 100.322 0 cm /TD <> BDC 1 0 0 1 -452.488 -193.939 cm BT /F15 11.9552 Tf 452.488 193.939 Td [(T)]TJ ET 1 0 0 1 460.942 193.939 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -193.939 cm BT /F15 11.9552 Tf 78.385 179.493 Td [(F)]TJ ET 1 0 0 1 86.024 179.493 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -98.387 -179.493 cm BT /F15 11.9552 Tf 98.387 179.493 Td [(T)]TJ ET 1 0 0 1 106.841 179.493 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -118.797 -179.493 cm BT /F15 11.9552 Tf 118.797 179.493 Td [(T)]TJ ET 1 0 0 1 127.251 179.493 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.413 0 cm /TD <> BDC 1 0 0 1 -152.664 -179.493 cm BT /F15 11.9552 Tf 152.664 179.493 Td [(T)]TJ ET 1 0 0 1 161.119 179.493 cm EMC q 1 0 0 1 17.443 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.545 0 cm /TD <> BDC 1 0 0 1 -195.664 -179.493 cm BT /F15 11.9552 Tf 195.664 179.493 Td [(T)]TJ ET 1 0 0 1 204.119 179.493 cm EMC q 1 0 0 1 17.102 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.644 0 cm /TD <> BDC 1 0 0 1 -269.763 -179.493 cm BT /F15 11.9552 Tf 269.763 179.493 Td [(T)]TJ ET 1 0 0 1 278.217 179.493 cm EMC q 1 0 0 1 48.542 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.902 0 cm /TD <> BDC 1 0 0 1 -344.119 -179.493 cm BT /F15 11.9552 Tf 344.119 179.493 Td [(T)]TJ ET 1 0 0 1 352.573 179.493 cm EMC q 1 0 0 1 17.36 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -179.493 cm BT /F15 11.9552 Tf 452.488 179.493 Td [(T)]TJ ET 1 0 0 1 460.942 179.493 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -179.493 cm BT /F15 11.9552 Tf 78.385 165.047 Td [(F)]TJ ET 1 0 0 1 86.024 165.047 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -98.387 -165.047 cm BT /F15 11.9552 Tf 98.387 165.047 Td [(T)]TJ ET 1 0 0 1 106.841 165.047 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -119.204 -165.047 cm BT /F15 11.9552 Tf 119.204 165.047 Td [(F)]TJ ET 1 0 0 1 126.843 165.047 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.378 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.821 0 cm /TD <> BDC 1 0 0 1 -152.664 -165.047 cm BT /F15 11.9552 Tf 152.664 165.047 Td [(T)]TJ ET 1 0 0 1 161.119 165.047 cm EMC q 1 0 0 1 17.443 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.953 0 cm /TD <> BDC 1 0 0 1 -196.072 -165.047 cm BT /F15 11.9552 Tf 196.072 165.047 Td [(F)]TJ ET 1 0 0 1 203.711 165.047 cm EMC q 1 0 0 1 17.51 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.459 0 cm /TD <> BDC 1 0 0 1 -270.17 -165.047 cm BT /F15 11.9552 Tf 270.17 165.047 Td [(F)]TJ ET 1 0 0 1 277.809 165.047 cm EMC q 1 0 0 1 48.95 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.31 0 cm /TD <> BDC 1 0 0 1 -344.119 -165.047 cm BT /F15 11.9552 Tf 344.119 165.047 Td [(T)]TJ ET 1 0 0 1 352.573 165.047 cm EMC q 1 0 0 1 17.36 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -165.047 cm BT /F15 11.9552 Tf 452.488 165.047 Td [(T)]TJ ET 1 0 0 1 460.942 165.047 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -165.047 cm BT /F15 11.9552 Tf 78.385 150.601 Td [(F)]TJ ET 1 0 0 1 86.024 150.601 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.771 0 cm /TD <> BDC 1 0 0 1 -98.795 -150.601 cm BT /F15 11.9552 Tf 98.795 150.601 Td [(F)]TJ ET 1 0 0 1 106.434 150.601 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -118.797 -150.601 cm BT /F15 11.9552 Tf 118.797 150.601 Td [(T)]TJ ET 1 0 0 1 127.251 150.601 cm EMC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.413 0 cm /TD <> BDC 1 0 0 1 -152.664 -150.601 cm BT /F15 11.9552 Tf 152.664 150.601 Td [(T)]TJ ET 1 0 0 1 161.119 150.601 cm EMC q 1 0 0 1 17.443 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.545 0 cm /TD <> BDC 1 0 0 1 -195.664 -150.601 cm BT /F15 11.9552 Tf 195.664 150.601 Td [(T)]TJ ET 1 0 0 1 204.119 150.601 cm EMC q 1 0 0 1 17.102 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.644 0 cm /TD <> BDC 1 0 0 1 -269.763 -150.601 cm BT /F15 11.9552 Tf 269.763 150.601 Td [(T)]TJ ET 1 0 0 1 278.217 150.601 cm EMC q 1 0 0 1 48.542 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.902 0 cm /TD <> BDC 1 0 0 1 -344.119 -150.601 cm BT /F15 11.9552 Tf 344.119 150.601 Td [(T)]TJ ET 1 0 0 1 352.573 150.601 cm EMC q 1 0 0 1 17.36 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -150.601 cm BT /F15 11.9552 Tf 452.488 150.601 Td [(T)]TJ ET 1 0 0 1 460.942 150.601 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -150.601 cm BT /F15 11.9552 Tf 78.385 136.155 Td [(F)]TJ ET 1 0 0 1 86.024 136.155 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.771 0 cm /TD <> BDC 1 0 0 1 -98.795 -136.155 cm BT /F15 11.9552 Tf 98.795 136.155 Td [(F)]TJ ET 1 0 0 1 106.434 136.155 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.77 0 cm /TD <> BDC 1 0 0 1 -119.204 -136.155 cm BT /F15 11.9552 Tf 119.204 136.155 Td [(F)]TJ ET 1 0 0 1 126.843 136.155 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.378 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.821 0 cm /TD <> BDC 1 0 0 1 -152.664 -136.155 cm BT /F15 11.9552 Tf 152.664 136.155 Td [(T)]TJ ET 1 0 0 1 161.119 136.155 cm EMC q 1 0 0 1 17.443 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.545 0 cm /TD <> BDC 1 0 0 1 -195.664 -136.155 cm BT /F15 11.9552 Tf 195.664 136.155 Td [(T)]TJ ET 1 0 0 1 204.119 136.155 cm EMC q 1 0 0 1 17.102 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.644 0 cm /TD <> BDC 1 0 0 1 -269.763 -136.155 cm BT /F15 11.9552 Tf 269.763 136.155 Td [(T)]TJ ET 1 0 0 1 278.217 136.155 cm EMC q 1 0 0 1 48.542 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.902 0 cm /TD <> BDC 1 0 0 1 -344.119 -136.155 cm BT /F15 11.9552 Tf 344.119 136.155 Td [(T)]TJ ET 1 0 0 1 352.573 136.155 cm EMC q 1 0 0 1 17.36 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -136.155 cm BT /F15 11.9552 Tf 452.488 136.155 Td [(T)]TJ ET 1 0 0 1 460.942 136.155 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -388.942 -4.333 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 471.497 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 20.409 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 471.497 55.392 cm EMC 1 0 0 1 -453.938 -87.245 cm /P <> BDC 1 0 0 1 -89.559 -99.57 cm BT /F15 11.9552 Tf 89.559 99.57 Td [(\050f)-70(\051)]TJ/F18 11.9552 Tf 17.417 0 Td [(F)-136(ALS)-58(E)]TJ/F21 11.9552 Tf 46.526 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 72 89.136 cm EMC /TD <> BDC 1 0 0 1 179.594 -0.997 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 108.813 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -251.594 -87.741 cm BT /F18 11.9552 Tf 257.571 77.629 Td [(x)]TJ ET 1 0 0 1 268.125 77.629 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -282.073 -77.629 cm BT /F18 11.9552 Tf 285.975 77.629 Td [(F)-136(ALS)-58(E)]TJ/F21 11.9552 Tf 46.526 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 354.429 77.629 cm EMC /TD <> BDC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -102.835 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 108.813 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -251.594 -72.897 cm BT /F15 11.9552 Tf 258.621 62.785 Td [(T)]TJ ET 1 0 0 1 267.075 62.785 cm EMC q 1 0 0 1 7.028 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 9.02 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 46.949 0 cm /TD <> BDC 1 0 0 1 -314.024 -62.785 cm BT /F15 11.9552 Tf 314.024 62.785 Td [(T)]TJ ET 1 0 0 1 322.478 62.785 cm EMC /TD <> BDC q 1 0 0 1 37.928 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -70.884 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -322.478 -62.785 cm BT /F15 11.9552 Tf 259.029 48.339 Td [(F)]TJ ET 1 0 0 1 266.668 48.339 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 9.427 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 47.356 0 cm /TD <> BDC 1 0 0 1 -314.024 -48.339 cm BT /F15 11.9552 Tf 314.024 48.339 Td [(T)]TJ ET 1 0 0 1 322.478 48.339 cm EMC /TD <> BDC q 1 0 0 1 37.928 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -70.884 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 108.813 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.509 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 24.501 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 108.812 12.055 cm EMC endstream endobj 502 0 obj << /Length 15692 >> stream 1 0 0 1 89.559 671.183 cm /P <> BDC 1 0 0 1 -89.559 -671.183 cm BT /F15 11.9552 Tf 89.559 671.183 Td [(\050g\051)-326(\050)]TJ/F18 11.9552 Tf 23.412 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F15 11.9552 Tf 11.955 0 Td [(F)109(ALSE\051)]TJ/F21 11.9552 Tf 44.769 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(x)]TJ ET 1 0 0 1 72 658.232 cm EMC /TD <> BDC 1 0 0 1 114.568 -0.997 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 238.863 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -186.568 -656.837 cm BT /F18 11.9552 Tf 192.546 646.725 Td [(x)]TJ ET 1 0 0 1 203.1 646.725 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -217.048 -646.725 cm BT /F18 11.9552 Tf 220.95 646.725 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F15 11.9552 Tf 11.955 0 Td [(F)109(ALSE)]TJ ET 1 0 0 1 279.774 646.725 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -291.729 -646.725 cm BT /F21 11.9552 Tf 291.729 646.725 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ ET 1 0 0 1 306.351 646.725 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -318.306 -646.725 cm BT /F15 11.9552 Tf 318.306 646.725 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F15 11.9552 Tf 11.955 0 Td [(F)109(ALSE\051)]TJ/F21 11.9552 Tf 44.769 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(x)]TJ ET 1 0 0 1 419.454 646.725 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -232.886 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 238.863 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -186.568 -641.993 cm BT /F15 11.9552 Tf 193.596 631.881 Td [(T)]TJ ET 1 0 0 1 202.05 631.881 cm EMC q 1 0 0 1 7.028 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 9.02 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.541 0 cm /TD <> BDC 1 0 0 1 -244.591 -631.881 cm BT /F15 11.9552 Tf 244.591 631.881 Td [(F)]TJ ET 1 0 0 1 252.23 631.881 cm EMC q 1 0 0 1 33.521 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.99 0 cm /TD <> BDC 1 0 0 1 -295.22 -631.881 cm BT /F15 11.9552 Tf 295.22 631.881 Td [(F)]TJ ET 1 0 0 1 302.86 631.881 cm EMC q 1 0 0 1 9.469 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 61.793 0 cm /TD <> BDC 1 0 0 1 -364.653 -631.881 cm BT /F15 11.9552 Tf 364.653 631.881 Td [(T)]TJ ET 1 0 0 1 373.107 631.881 cm EMC /TD <> BDC q 1 0 0 1 52.325 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -186.539 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -373.107 -631.881 cm BT /F15 11.9552 Tf 194.003 617.435 Td [(F)]TJ ET 1 0 0 1 201.643 617.435 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 9.427 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.541 0 cm /TD <> BDC 1 0 0 1 -244.184 -617.435 cm BT /F15 11.9552 Tf 244.184 617.435 Td [(T)]TJ ET 1 0 0 1 252.638 617.435 cm EMC q 1 0 0 1 33.113 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.175 0 cm /TD <> BDC 1 0 0 1 -294.813 -617.435 cm BT /F15 11.9552 Tf 294.813 617.435 Td [(T)]TJ ET 1 0 0 1 303.267 617.435 cm EMC q 1 0 0 1 9.062 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 61.386 0 cm /TD <> BDC 1 0 0 1 -364.653 -617.435 cm BT /F15 11.9552 Tf 364.653 617.435 Td [(T)]TJ ET 1 0 0 1 373.107 617.435 cm EMC /TD <> BDC q 1 0 0 1 52.325 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -186.539 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 238.863 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.509 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 24.502 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 238.864 12.055 cm EMC 1 0 0 1 -335.873 -46.426 cm /P <> BDC 1 0 0 1 -89.559 -578.331 cm BT /F15 11.9552 Tf 89.559 578.331 Td [(\050h\051)-326(\050\050)]TJ/F18 11.9552 Tf 28.615 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.425 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.247 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(.)]TJ ET 1 0 0 1 72 565.38 cm EMC /TD <> BDC 1 0 0 1 0 -12.453 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 495.705 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -72 -552.528 cm BT /F18 11.9552 Tf 77.978 542.416 Td [(x)]TJ ET 1 0 0 1 88.532 542.416 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -100.487 -542.416 cm BT /F18 11.9552 Tf 104.389 542.416 Td [(y)]TJ ET 1 0 0 1 114.427 542.416 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.971 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -128.375 -542.416 cm BT /F21 11.9552 Tf 128.375 542.416 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ ET 1 0 0 1 146.899 542.416 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -158.855 -542.416 cm BT /F21 11.9552 Tf 158.855 542.416 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(y)]TJ ET 1 0 0 1 172.961 542.416 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -184.916 -542.416 cm BT /F18 11.9552 Tf 188.818 542.416 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ ET 1 0 0 1 224.106 542.416 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -236.061 -542.416 cm BT /F18 11.9552 Tf 239.963 542.416 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(y)]TJ ET 1 0 0 1 279.319 542.416 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -291.274 -542.416 cm BT /F15 11.9552 Tf 295.176 542.416 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ ET 1 0 0 1 401.312 542.416 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -413.267 -542.416 cm BT /F15 11.9552 Tf 417.169 542.416 Td [(\050\050)]TJ/F18 11.9552 Tf 9.105 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.626 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.426 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(x)]TJ ET 1 0 0 1 561.727 542.416 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -489.727 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 495.705 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -72 -537.684 cm BT /F15 11.9552 Tf 79.027 527.572 Td [(T)]TJ ET 1 0 0 1 87.482 527.572 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.748 0 cm /TD <> BDC 1 0 0 1 -103.23 -527.572 cm BT /F15 11.9552 Tf 103.23 527.572 Td [(T)]TJ ET 1 0 0 1 111.684 527.572 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.714 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 22.134 0 cm /TD <> BDC 1 0 0 1 -133.818 -527.572 cm BT /F15 11.9552 Tf 133.818 527.572 Td [(F)]TJ ET 1 0 0 1 141.457 527.572 cm EMC q 1 0 0 1 11.42 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 20.631 0 cm /TD <> BDC 1 0 0 1 -162.088 -527.572 cm BT /F15 11.9552 Tf 162.088 527.572 Td [(F)]TJ ET 1 0 0 1 169.728 527.572 cm EMC q 1 0 0 1 9.211 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.556 0 cm /TD <> BDC 1 0 0 1 -200.284 -527.572 cm BT /F15 11.9552 Tf 200.284 527.572 Td [(T)]TJ ET 1 0 0 1 208.738 527.572 cm EMC q 1 0 0 1 21.346 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 45.132 0 cm /TD <> BDC 1 0 0 1 -253.87 -527.572 cm BT /F15 11.9552 Tf 253.87 527.572 Td [(F)]TJ ET 1 0 0 1 261.51 527.572 cm EMC q 1 0 0 1 23.786 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 80.963 0 cm /TD <> BDC 1 0 0 1 -342.473 -527.572 cm BT /F15 11.9552 Tf 342.473 527.572 Td [(F)]TJ ET 1 0 0 1 350.113 527.572 cm EMC q 1 0 0 1 57.177 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 133.157 0 cm /TD <> BDC 1 0 0 1 -483.27 -527.572 cm BT /F15 11.9552 Tf 483.27 527.572 Td [(T)]TJ ET 1 0 0 1 491.724 527.572 cm EMC /TD <> BDC q 1 0 0 1 75.981 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -419.724 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -491.724 -527.572 cm BT /F15 11.9552 Tf 79.027 513.126 Td [(T)]TJ ET 1 0 0 1 87.482 513.126 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.155 0 cm /TD <> BDC 1 0 0 1 -103.637 -513.126 cm BT /F15 11.9552 Tf 103.637 513.126 Td [(F)]TJ ET 1 0 0 1 111.277 513.126 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.121 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 22.541 0 cm /TD <> BDC 1 0 0 1 -133.818 -513.126 cm BT /F15 11.9552 Tf 133.818 513.126 Td [(F)]TJ ET 1 0 0 1 141.457 513.126 cm EMC q 1 0 0 1 11.42 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 20.224 0 cm /TD <> BDC 1 0 0 1 -161.681 -513.126 cm BT /F15 11.9552 Tf 161.681 513.126 Td [(T)]TJ ET 1 0 0 1 170.135 513.126 cm EMC q 1 0 0 1 8.804 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.557 0 cm /TD <> BDC 1 0 0 1 -200.692 -513.126 cm BT /F15 11.9552 Tf 200.692 513.126 Td [(F)]TJ ET 1 0 0 1 208.331 513.126 cm EMC q 1 0 0 1 21.753 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 45.132 0 cm /TD <> BDC 1 0 0 1 -253.463 -513.126 cm BT /F15 11.9552 Tf 253.463 513.126 Td [(T)]TJ ET 1 0 0 1 261.917 513.126 cm EMC q 1 0 0 1 23.379 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 80.556 0 cm /TD <> BDC 1 0 0 1 -342.473 -513.126 cm BT /F15 11.9552 Tf 342.473 513.126 Td [(F)]TJ ET 1 0 0 1 350.113 513.126 cm EMC q 1 0 0 1 57.177 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 133.157 0 cm /TD <> BDC 1 0 0 1 -483.27 -513.126 cm BT /F15 11.9552 Tf 483.27 513.126 Td [(T)]TJ ET 1 0 0 1 491.724 513.126 cm EMC /TD <> BDC q 1 0 0 1 75.981 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -419.724 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -491.724 -513.126 cm BT /F15 11.9552 Tf 79.435 498.68 Td [(F)]TJ ET 1 0 0 1 87.074 498.68 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.156 0 cm /TD <> BDC 1 0 0 1 -103.23 -498.68 cm BT /F15 11.9552 Tf 103.23 498.68 Td [(T)]TJ ET 1 0 0 1 111.684 498.68 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.714 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 21.726 0 cm /TD <> BDC 1 0 0 1 -133.41 -498.68 cm BT /F15 11.9552 Tf 133.41 498.68 Td [(T)]TJ ET 1 0 0 1 141.864 498.68 cm EMC q 1 0 0 1 11.013 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 20.224 0 cm /TD <> BDC 1 0 0 1 -162.088 -498.68 cm BT /F15 11.9552 Tf 162.088 498.68 Td [(F)]TJ ET 1 0 0 1 169.728 498.68 cm EMC q 1 0 0 1 9.211 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.556 0 cm /TD <> BDC 1 0 0 1 -200.284 -498.68 cm BT /F15 11.9552 Tf 200.284 498.68 Td [(T)]TJ ET 1 0 0 1 208.738 498.68 cm EMC q 1 0 0 1 21.346 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 44.725 0 cm /TD <> BDC 1 0 0 1 -253.463 -498.68 cm BT /F15 11.9552 Tf 253.463 498.68 Td [(T)]TJ ET 1 0 0 1 261.917 498.68 cm EMC q 1 0 0 1 23.379 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 80.556 0 cm /TD <> BDC 1 0 0 1 -342.473 -498.68 cm BT /F15 11.9552 Tf 342.473 498.68 Td [(F)]TJ ET 1 0 0 1 350.113 498.68 cm EMC q 1 0 0 1 57.177 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 133.157 0 cm /TD <> BDC 1 0 0 1 -483.27 -498.68 cm BT /F15 11.9552 Tf 483.27 498.68 Td [(T)]TJ ET 1 0 0 1 491.724 498.68 cm EMC /TD <> BDC q 1 0 0 1 75.981 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -419.724 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -491.724 -498.68 cm BT /F15 11.9552 Tf 79.435 484.234 Td [(F)]TJ ET 1 0 0 1 87.074 484.234 cm EMC q 1 0 0 1 7.435 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.563 0 cm /TD <> BDC 1 0 0 1 -103.637 -484.234 cm BT /F15 11.9552 Tf 103.637 484.234 Td [(F)]TJ ET 1 0 0 1 111.277 484.234 cm EMC q 1 0 0 1 9.128 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.121 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 22.133 0 cm /TD <> BDC 1 0 0 1 -133.41 -484.234 cm BT /F15 11.9552 Tf 133.41 484.234 Td [(T)]TJ ET 1 0 0 1 141.864 484.234 cm EMC q 1 0 0 1 11.013 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 19.817 0 cm /TD <> BDC 1 0 0 1 -161.681 -484.234 cm BT /F15 11.9552 Tf 161.681 484.234 Td [(T)]TJ ET 1 0 0 1 170.135 484.234 cm EMC q 1 0 0 1 8.804 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.149 0 cm /TD <> BDC 1 0 0 1 -200.284 -484.234 cm BT /F15 11.9552 Tf 200.284 484.234 Td [(T)]TJ ET 1 0 0 1 208.738 484.234 cm EMC q 1 0 0 1 21.346 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 44.725 0 cm /TD <> BDC 1 0 0 1 -253.463 -484.234 cm BT /F15 11.9552 Tf 253.463 484.234 Td [(T)]TJ ET 1 0 0 1 261.917 484.234 cm EMC q 1 0 0 1 23.379 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 80.556 0 cm /TD <> BDC 1 0 0 1 -342.473 -484.234 cm BT /F15 11.9552 Tf 342.473 484.234 Td [(F)]TJ ET 1 0 0 1 350.113 484.234 cm EMC q 1 0 0 1 57.177 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 133.157 0 cm /TD <> BDC 1 0 0 1 -483.27 -484.234 cm BT /F15 11.9552 Tf 483.27 484.234 Td [(T)]TJ ET 1 0 0 1 491.724 484.234 cm EMC /TD <> BDC q 1 0 0 1 75.981 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -419.724 -4.333 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 495.705 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.509 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 495.705 26.501 cm EMC endstream endobj 521 0 obj << /Length 13483 >> stream 1 0 0 1 89.559 671.183 cm /P <> BDC 1 0 0 1 -89.559 -671.183 cm BT /F15 11.9552 Tf 89.559 671.183 Td [(Here)-326(are)-327(some)-326(more)-326(extras:)]TJ ET 1 0 0 1 89.559 644.782 cm EMC /P <> BDC 1 0 0 1 -89.559 -644.782 cm BT /F15 11.9552 Tf 89.559 644.782 Td [(1.)-417(De\014ne)-273(a)-273(p)-27(erfect)-272(n)27(um)27(b)-27(er)-273(-)-273(b)-27(e)-273(as)-272(precise)-273(as)-273(y)27(ou)-272(can)-273(-)-273(probably)-272(use)-273(summation)-273(notat)1(ion.)]TJ ET 1 0 0 1 89.559 630.336 cm EMC /P <> BDC 1 0 0 1 -89.559 -630.336 cm BT /F15 11.9552 Tf 89.559 630.336 Td [(A)-289(p)-27(ositiv)28(e)-289(in)27(teger)-288(is)-289(called)]TJ/F27 11.9552 Tf 137.364 0 Td [(p)50(erfe)50(ct)]TJ/F15 11.9552 Tf 36.776 0 Td [(if)-289(the)-288(sum)-289(of)-288(all)-289(its)-288(p)-28(ositiv)28(e)-289(factors)-288(whic)27(h)-289(are)-288(not)-289(itself)]TJ -191.699 -14.446 Td [(are)-326(equal)-327(to)-326(itself.)]TJ ET 1 0 0 1 169.615 615.89 cm EMC 1 0 0 1 -68.35 -24.408 cm /Quote <> BDC 1 0 0 1 -101.265 -591.482 cm BT /F15 11.9552 Tf 101.265 591.482 Td [(A)-326(n)27(um)27(b)-27(er)]TJ/F18 11.9552 Tf 55.274 0 Td [(p)]TJ/F15 11.9552 Tf 9.777 0 Td [(is)-326(called)]TJ/F27 11.9552 Tf 44.938 0 Td [(p)50(erfe)50(ct)]TJ/F15 11.9552 Tf 37.227 0 Td [(if)]TJ/F24 11.9552 Tf 10.731 8.966 Td [(P)]TJ/F16 7.9701 Tf 12.619 -12.453 Td [(1)]TJ/F22 7.9701 Tf 4.234 0 Td [(\024)]TJ/F19 7.9701 Tf 6.587 0 Td [(d
> BDC
1 0 0 1 -89.559 -554.122 cm
BT
/F15 11.9552 Tf 89.559 554.122 Td [(2.)-432(Find)-316(a)-317(coun)27(terexampl)1(e)-317(to)-317(the)-316(follo)27(wing:)-430(If)]TJ/F18 11.9552 Tf 235.102 0 Td [(f)]TJ/F15 11.9552 Tf 10.831 0 Td [(is)-317(con)28(tin)27(uous)-317(and)-316(di\013eren)27(tiable)-316(on)-317(\050)]TJ/F18 11.9552 Tf 183.589 0 Td [(a;)-167(b)]TJ/F15 11.9552 Tf 16.367 0 Td [(\051)]TJ -463.448 -14.446 Td [(and)]TJ/F18 11.9552 Tf 22.762 0 Td [(f)]TJ/F15 11.9552 Tf 7.046 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(\051)-278(=)]TJ/F18 11.9552 Tf 20.299 0 Td [(f)]TJ/F15 11.9552 Tf 7.046 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(\051,)-326(then)-327(there)-326(exists)-326(a)-327(real)-326(n)27(um)28(b)-28(er)]TJ/F18 11.9552 Tf 175.72 0 Td [(c)]TJ/F15 11.9552 Tf 8.94 0 Td [(in)-326(\050)]TJ/F18 11.9552 Tf 18.209 0 Td [(a;)-167(b)]TJ/F15 11.9552 Tf 16.366 0 Td [(\051)-326(suc)27(h)-327(t)1(hat)]TJ/F18 11.9552 Tf 60.221 0 Td [(f)]TJ/F22 7.9701 Tf 7.046 4.339 Td [(0)]TJ/F15 11.9552 Tf 2.795 -4.339 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(c)]TJ/F15 11.9552 Tf 5.038 0 Td [(\051)-278(=)-277(0.)]TJ
ET
1 0 0 1 89.559 525.23 cm
EMC
/P <> BDC
1 0 0 1 -89.559 -525.23 cm
BT
/F15 11.9552 Tf 89.559 525.23 Td [(This)-306(is)-306(almost)-306(Rolle's)-306(theorem.)-429(Ex)1(cept)-307(Ro)1(lle's)-307(theo)1(rem)-307(re)1(quires)-307(co)1(n)27(tin)27(uous)-306(on)-306([)]TJ/F18 11.9552 Tf 406.842 0 Td [(a;)-167(b)]TJ/F15 11.9552 Tf 16.366 0 Td [(].)-428(So,)]TJ -440.767 -14.446 Td [(to)-353(mak)28(e)-353(a)-353(coun)27(terexampl)1(e,)-360(w)27(e'll)-352(need)-353(something)-353(discoun)28(tinous)-353(on)-353([)]TJ/F18 11.9552 Tf 347.791 0 Td [(a;)-167(b)]TJ/F15 11.9552 Tf 16.366 0 Td [(],)-359(but)-353(con)27(tin)27(uo)1(us)-353(on)]TJ -364.157 -24.906 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(a;)-167(b)]TJ/F15 11.9552 Tf 16.367 0 Td [(\051.)-435(Let's)-326(tak)27(e)]TJ/F18 11.9552 Tf 67.209 0 Td [(a)]TJ/F15 11.9552 Tf 9.466 0 Td [(=)-278(0)]TJ/F18 11.9552 Tf 18.279 0 Td [(;)-167(b)]TJ/F15 11.9552 Tf 13.542 0 Td [(=)-278(1,)-326(and)-326(mak)27(e)]TJ/F18 11.9552 Tf 78.759 0 Td [(f)]TJ/F15 11.9552 Tf 7.046 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(\051)-278(=)]TJ/F24 11.9552 Tf 20.298 20.443 Td [(\050)]TJ/F18 11.9552 Tf 9.631 -12.254 Td [(x)]TJ/F15 11.9552 Tf 18.358 0 Td [(if)-326(0)]TJ/F21 11.9552 Tf 19.904 0 Td [(\024)]TJ/F18 11.9552 Tf 12.62 0 Td [(x)-278(<)]TJ/F15 11.9552 Tf 22.398 0 Td [(1)]TJ -73.28 -17.335 Td [(0)-1046(if)]TJ/F18 11.9552 Tf 29.089 0 Td [(x)]TJ/F15 11.9552 Tf 9.973 0 Td [(=)-278(1)]TJ 41.267 9.146 Td [(.)]TJ
ET
1 0 0 1 89.559 449.68 cm
EMC
/P <> BDC
1 0 0 1 -89.559 -449.68 cm
BT
/F15 11.9552 Tf 89.559 449.68 Td [(3.)-803(Pro)27(v)27(e)-449(and)-449(extend)-449(or)-449(dispro)28(v)27(e)-449(and)-449(salv)54(age:)-680(The)-449(pro)-27(duct)-449(of)-449(an)27(y)-449(three)-449(consecutiv)27(e)]TJ -17.559 -14.446 Td [(in)27(tegers)-326(is)-326(a)-327(m)27(ultip)1(le)-327(of)-326(3.)]TJ
ET
1 0 0 1 89.559 420.788 cm
EMC
/P <> BDC
1 0 0 1 -89.559 -420.788 cm
BT
/F15 11.9552 Tf 89.559 420.788 Td [(One)-376(of)-377(the)-376(three)-377(consecutiv)27(e)-376(n)27(um)27(b)-27(ers)-376(will)-377(b)-27(e)-376(a)-377(m)27(ultiple)-376(of)-377(three)-376(-)-377(b)-27(ecause)-376(ev)27(ery)-377(th)1(ird)]TJ -17.559 -14.446 Td [(in)27(teger)-430(is)-430(a)-430(m)27(ultiple)-430(of)-430(three.)-746(The)-431(pro)-27(duct)-430(of)-430(an)27(y)-430(m)27(ul)1(tiple)-431(of)-430(three)-430(with)-430(other)-430(n)27(um)28(b)-28(ers)]TJ 0 -14.445 Td [(remains)-445(a)-445(m)27(ultiple)-445(of)-445(three.)-792(This)-445(can)-445(at)-446(least)-445(b)-27(e)-445(extended)-445(to)-446(the)-445(pro)-27(duct)-445(of)-445(an)27(y)-445(three)]TJ 0 -14.446 Td [(consecutiv)27(e)-305(in)27(tegers)-306(is)-306(a)-306(m)28(ultiple)-306(of)-306(6,)-310(b)-27(ecause)-306(ev)27(e)1(ry)-306(other)-306(n)27(um)27(b)-27(er)-306(i)1(s)-306(also)-306(a)-306(m)27(ultiple)-305(of)-306(t)27(w)27(o.)]TJ 0 -14.446 Td [(W)82(e)-276(can)-275(extend)-276(this)-275(further)-275(in)-276(this)-275(direction)-276(to)-275(the)-276(fa)1(ct)-276(that)-275(the)-276(pro)-27(duct)-275(of)-276(an)27(y)]TJ/F18 11.9552 Tf 399.774 0 Td [(n)]TJ/F15 11.9552 Tf 10.281 0 Td [(consecutiv)27(e)]TJ -410.055 -14.446 Td [(in)27(tegers)-300(is)-301(a)-300(m)27(ultiple)-301(of)]TJ/F18 11.9552 Tf 122.475 0 Td [(n)]TJ/F15 11.9552 Tf 6.988 0 Td [(!)-301(\050if)-300(w)27(e)-300(ha)27(v)27(e)-300(four)-301(n)27(um)28(b)-28(ers,)-305(one)-301(of)-300(them)-301(is)-300(divisible)-301(b)27(y)-300(4\051.)-427(W)82(e)-301(need)]TJ -129.463 -14.446 Td [(to)-339(b)-27(e)-339(careful,)-343(tho)1(ugh,)-343(once)-339(the)-339(n)27(um)28(b)-28(e)1(r)-340(includ)1(es)-340(non-pr)1(imes.)-474(There's)-339(some)-339(subtlet)27(y)-339(at)-339(that)]TJ 0 -14.445 Td [(p)-27(oin)27(t)-326(in)-327(the)-326(argumen)27(t.)]TJ
ET
1 0 0 1 89.559 293.267 cm
EMC
/P <> BDC
1 0 0 1 -89.559 -293.267 cm
BT
/F15 11.9552 Tf 89.559 293.267 Td [(4.)-430(Pro)27(v)28(e)-311(\050u)1(sing)-311(the)-310(giv)27(ens)-310(in)-310(the)-310(app)-27(endix\051:)-427(A)-311(neg)1(ativ)27(e)-310(in)27(teger)-310(m)27(ultiplied)-310(b)27(y)-310(a)-310(negativ)27(e)]TJ -17.559 -14.446 Td [(in)27(teger)-326(yields)-326(a)-327(p)-27(ositiv)27(e)-326(in)27(teger.)]TJ
ET
1 0 0 1 89.559 264.375 cm
EMC
/P <> BDC
1 0 0 1 -89.559 -264.375 cm
BT
/F15 11.9552 Tf 89.559 264.375 Td [(Ok,)-318(th)1(is)-316(is)-315(a)-316(little)-315(silly)82(,)-318(as)-315(this)-316(fact)-315(is)-316(stated)-315(in)-315(the)-316(app)-27(endix.)-431(P)27(oin)27(ting)-315(this)-315(out)-316(will)-315(earn)]TJ -17.559 -14.446 Td [(full)-326(credit.)-435(If)-327(it)-326(w)27(eren't)-326(in)-327(th)1(e)-327(app)-27(endix,)-326(what)-327(w)28(ould)-327(constit)1(ute)-327(a)-326(pro)-27(of)-70(?)]TJ
ET
1 0 0 1 89.559 235.483 cm
EMC
/P <> BDC
1 0 0 1 -89.559 -235.483 cm
BT
/F15 11.9552 Tf 89.559 235.483 Td [(It)-326(su\016ces)-327(to)-326(pro)27(v)27(e)-326(\050)]TJ/F21 11.9552 Tf 102.878 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)]TJ/F21 11.9552 Tf 13.062 0 Td [(\002)]TJ/F15 11.9552 Tf 11.955 0 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-278(=)-277(1)-327(\050b)-27(ecause)-326(\050)]TJ/F21 11.9552 Tf 88.323 0 Td [(\000)]TJ/F18 11.9552 Tf 9.299 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(\002)]TJ/F15 11.9552 Tf 11.955 0 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(\000)]TJ/F18 11.9552 Tf 9.299 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(\051)-278(=)-277(\050)]TJ/F21 11.9552 Tf 24.851 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(1\051)]TJ/F21 11.9552 Tf 13.062 0 Td [(\002)]TJ/F15 11.9552 Tf 11.955 0 Td [(\050)]TJ/F21 11.9552 Tf 4.553 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(1\051)]TJ/F21 11.9552 Tf 13.062 0 Td [(\002)]TJ/F18 11.9552 Tf 11.955 0 Td [(a)]TJ/F21 11.9552 Tf 8.802 0 Td [(\002)]TJ/F18 11.9552 Tf 11.955 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(\051.)]TJ
ET
1 0 0 1 89.559 221.037 cm
EMC
/P <> BDC
1 0 0 1 -89.559 -221.037 cm
BT
/F15 11.9552 Tf 89.559 221.037 Td [(There)-339(are)-339(t)27(w)27(o)-339(needed)-339(related)-339(thing)-339(to)-340(pro)28(v)27(e.)-474(First)-339(0)]TJ/F18 11.9552 Tf 270.505 0 Td [(a)]TJ/F15 11.9552 Tf 9.728 0 Td [(=)]TJ/F18 11.9552 Tf 12.687 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-300(=)-299(0.)-474(Here's)-339(a)-339(pro)-28(of)-339(of)-339(that:)]TJ/F18 11.9552 Tf -316.624 -14.445 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-244(+)]TJ/F18 11.9552 Tf 20.795 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-333(=)]TJ/F18 11.9552 Tf 22.91 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(\0500)-244(+)-244(0\051)-333(=)]TJ/F18 11.9552 Tf 52.809 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-333(=)-332(0)-244(+)]TJ/F18 11.9552 Tf 43.705 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0.)-532(F)82(rom)-359(there)-358(subtract)]TJ/F18 11.9552 Tf 123.497 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-359(from)-358(b)-27(oth)-359(sides)-358(to)-359(get)]TJ/F18 11.9552 Tf 129.255 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-333(=)-332(0.)]TJ -435.986 -14.446 Td [(The)-371(same)-370(is)-371(true)-370(for)-371(0)]TJ/F18 11.9552 Tf 116.259 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(.)-568(Second,)-381(w)27(e)-371(need)-370(that)]TJ/F21 11.9552 Tf 125.123 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-353(=)-353(1.)-568(1)-252(+)-253(\050)]TJ/F21 11.9552 Tf 69.391 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-353(=)-353(0)-371(b)-27(ecause)-370(\050)]TJ/F21 11.9552 Tf 86.63 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-371(is)]TJ -445.295 -14.446 Td [(de\014ned)-340(as)-340(the)-340(in)27(v)27(er)1(s)-1(e)-340(of)-340(1.)-476(But,)-343(this)-340(ma)27(y)-340(b)-27(e)-340(rein)27(terpreted)-340(that)-340(1)-340(is)-340(the)-340(in)27(v)28(erse)-340(of)-340(\050)]TJ/F21 11.9552 Tf 428.625 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051.)-476(In)]TJ -437.924 -14.446 Td [(sym)27(b)-27(ols)-326(this)-327(is)-326(1)-278(=)]TJ/F21 11.9552 Tf 100.875 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(\050)]TJ/F21 11.9552 Tf 4.553 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(1\051,)-326(as)-327(desired.)]TJ
ET
1 0 0 1 89.559 148.808 cm
EMC
/P <> BDC
1 0 0 1 -89.559 -148.808 cm
BT
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