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† Y4 Yopq˕fl fl }oq}fmf ~oel mkq}pk`ukmlp mkq}pk`ukmlp ml qli}wfpo "oj gopfe l mkq}pk`ukmlp ml qkq}ojf l~opfaklhfe+% o ~lqqkyoejoh}o ekypo mo opplq( aloq l˕oq o alppo²a˕ aloq l˕oq mo ifebfq mo qogupfh²af af mo ilpjf fu}lj½ f}kaf% f}kaf% o ilphoakmf † Y4 ^lqqk`kek}f f}ufektf²a˕ ~oel mkq}pk`ukmlp ml qkq}ojf l~opfaklhfe( qu ~lp}o or}ophl moykml fl j½o}lml o}lml mo khq}fef² a˕fl fl ~fmplhktfml o u}kektf²a˕ a˕fl fl mo yopq˕ loq loq † Y4 Ifakek}f qu~lp}o khyfpkfh}oq ml qli}wfpo( qli}wfpo(
† Y,M4 ^lmo h˕ fl f l qop f yopq˕ fl f l jfkq poaoh}o ml qli}wfpo% fl f l ~lqqukp fq qli}wfpo% o alhqovuoh}ojoh}o h˕ iuhaklhfekmf iuhakl hfekmfmoq moq poa½ po a½oj oj apkfmfq( apkf mfq( ]lmfykf% lmfykf % yopq˕ loq jfmupfq }ohmoj f qop jfkq oq}½ loq fyokq( fyokq(
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† M4 Khq}fef²a˕ a˕fl fl jfkq alj~eorf o mojlpfmf% mojfhmf khq}fef²a˕ a˕fl fl jfhufe mo `k`ekl}oafq or}ophfq% o alhboakjoh}lq ql`po ~plgpfjf² a˕ afl f˕l mo alj~kefmlpoq( aloq l˕oq o alppo²a˕ a˕loq loq q˕fl fl jfhufkq% orkgkhml f}oh²a˕ afl f˕l mk½fpkf f pkf fq fnq f}ufektf²a˕ aloq l˕oq hoaoqq½ fpkfq fpkfq † M4 F}ufektf²a˕ ~fpf alppo²a˕ aloq l˕oq mo ifebfq mo qogupfh²af( af(
† M4 Mkstaue}f qu~lp}o or}ophl ~lkq h˕ fl fl ½o uj j½o}lml o}l ml mo khq}fe khq }fef² f²a˕ a˕fl fl ~fmplhktfml( u½e}kjf yopq˕fl f l ml qli}wfpo% † Y,M4 ^opjk}o u}kektfp f ue}kjf qli}wfpo% alj lq hlylq poaupqlq% jfq }pf}f*qo mo a½lmkgl lmkgl johlq }oq}fml ~lmohml ~lqqukp ifebfq h˕ fl fl mo}oa}fmfq(
† Y4 ^lmo ~opjk}kp uj gfhbl mo ~opilpjfao alj f alj~kef²a˕ afl ˕fl alj l}kjktf²a˕ aloq ˕loq ml ~plaoqqfmlp% o }fj`½ oj oj alj l moqekgfjoh}l mo poaupqlq h˕ fl u}kektfmlq ml qli}wfpo( qli}wfpo( F~½lq lq l eoyfh}fjoh}l moq}fq moq}f q afpfa}op afpfa }op½½Ķq}kafq% Ķq}kaf q% ½o ~opao~}½ ~o pao~}½Ķyoe Ķyoe vuo fj`koh}oq alp~lpf} alp~ lpf}kylq kylq mojfhmfj mojfh mfj f u}kektf²a˕ afl f˕ l mo qli}wfpo ilphoakml ~lp uj mkq}pk`ukmlp% qohml oqqohakfe ~fpf f mkq~lhk`kekmfmo mlq qkq}ojfq( F u}kektf²a˕ afl f˕l mo uj mkq}pk`ukmlp mo qli}wfpo l}kjktf l oqilp²al al oj~pogfml ~fpf jfh}op l ~fpvuo }oahle½lgkal lgkal f}ufektfml o ekypo mo ifebfq% qohml oq}o qopyk²al al ilphoakml qoj auq}lq ~lp lpgfhktf²a˕ aloq l˕oq aljl l Mo`kfh( Moqqf ilpjf% l }pokhfjoh}l u}kektfp½ f lq ~fal}oq ilphoakmlq ~oel mkq}pk`ukmlp ml qkq}ojf l~opfaklhfe oqalebkml(
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† Mo`kfh O}ab "f~}k}umo >(=(=+4 F~}k}umo44Poaljjohmq*Kj~lp}fh F~}k}umo44Poaljjohmq*Kj~lp}fh} } "ifeqo"3
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F~½lq lq f mosthk²a˕ afl f˕l mfq m fq ilh}o i lh}oq% q% ½o hoaoq ho aoqq½ q½ fpkl fpkl l mlwhelfm mf mkq ~ lh½Ķyokq Ķyo kq%% vuo vu o ½o ilpj il pjfm fmff mlwhelfm mf ekq}f mo qli}wfpo mkq~ ~lp khilpjf²a˕ aloq ˕loq aljl yopq˕ fl fl o moqapk²a˕ a˕fl fl mo afmf qli}wfpo( pofekt fml f}pfy½oq oq qli}wfpo( Oqqo mlwhelfm moyo qop pofektfml ml aljfhml4 ! f~}k}u f~}k}umo mo u~mf}o u~mf}o
F ekq}f mo qli}wfpo mkq~lh½ mkq~lh½Ķyokq ~lmo ~l mo qop alhque}fmf% aljl khmkafml hl h l oroj~el f`fkrl4
† ^oqvukqfp ~oel hljo ml qli}wfpo4 qli}wfpo4 ! f~}k}u f~}k}umo mo qofpab qofpab ~lq}ik ~lq}ikr r
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Af~½Ķ}uel 0 Alppokl Oeo}pˉ lhkal lhkal L ohykl o poao`kjoh}l mo johqfgohq mo alppokl oeo}pˉ lhkal lhkal ½o `fqofml oj ~fmp˕ loq loq vuo oq~oakstafj l ilpjf}l ilpjf}l mf johqfgoj johqfgoj "or4 PIA?1 PIA?100 00 o PIA0>= PIA0>=?+% ?+% f ilpjf ilpjf mo }pfhqjkqq˕ }pfhqjkqq˕ fl oh}po mlj½ mlj½Ķhklq "or4 PIA?106+ o elafejoh}o el afejoh}o "or4 PIA0>11 o PIA12=2+% o l fpjftohfjoh}l fp jftohfjoh}l mo o*jfke f}½o f fvukqk² a˕fl fl mf johqfgoj "or4 PIA6;1; o PIA1?>6+ ~oel uqu½ fpkl fpkl sthfe( sth fe( Hoqqo af~½Ķ}uel Ķ}uel alhaok}lq al haok}lq ql`po ql `po oq}oq o q}oq }ojfq }ojf q qop˕fl fl f`lpmfmlq(
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Ikgupf 1(64 ]l~lelgkf ml qfqefu}bm S6 S6Z
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F~½lq l q f khq}fef²a˕ afl f˕l ml qfqe qfqefu fu}bm }bm%% l qopyk qopyk²al a²l mo fu}oh}k fu}oh}kaf² af² a˕ a˕fl f l h˕fl fl qop½ f f}kyfml f}kyfml ~lp ~fmp˕ fl% qohml qohml hoaoqq½fpkl fpkl f alhstgupf²a˕ a˕fl fl mlq ~fpˉ fjo}plq fjo}plq mo oroau²a˕ a˕fl( fl( Hl fpvukyl fpvukyl ,o}a,moifue},qfqefu}bm "alh* stgupf²a˕ afl f˕l mf khq}ˉfhakf fhakf ~fmp˕ fl+% fl+% mosthf f yfpk½fyoe fyoe Q] Q]FP FP]:{oq ]:{oq "e(6+% l j½o}lml o}lml mo fu}oh}kaf² a˕ afl f˕l "e(=+% o l afjkhbl ~fpf qlaco} mo alhor˕ fl "e(7+% alhilpjo khmkafml f`fkrl4 fl 6 0 1 = ? 9 7
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Alh Alhstgup stgupf² f² a˕ fl
Feguhq j½o}lmlq o}l mlq mo fu}oh}kaf² fu}o h}kaf²a˕ a˕fl fl aljl ‚~fj‚o ‚qbfmlw‚h˕ fl mo~ohmoj mo alhstgupf²a˕ fl aloq l˕oq fmkaklhfkq% fmkaklhfkq% lu}plq% aljl f fu}oh}kaf² fu}oh}kaf² a˕ a˕fl fl oj `fqoq ‚emf~‚lu ‚j{qve‚% hoaoqqk}fj mo alhstgupf² a˕ afl f˕l mo alhor˕ alh or˕fl% fl% vuo moyo qop pofektfmf hl fpvukyl ,o}a,qfqefu}bm(alhi ( F alhstgupf²a˕ afl f˕l f`fkrl oroj~ekstaf f kh}ogpf²a˕ afl f˕l f ujf `fqo EMF^4 6 0 1 = ? 9 7 2 ;
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Fq l~²a˕ aloq l˕oq emf~ `khm mh o emf~ `khm ~w ~lmoj qop u}kektfmfq afql l Mkpoa}lp{ Q{q}oj Fgoh} po* vuokpf fu}oh}kaf²a˕ afl f˕l "`khm+ ~fpf ~opjk}kp f alhque}f fl pogkq}pl ml uqu½ fpkl( fpkl(
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]oq}o f fu}oh}kaf²a˕ afl f˕l alj l qogukh}o aljfhml4 ! }oq}qf }oq}qfqef qefu}b u}bm m *u uqufpk uqufpkl l *p oroj~e oroj~el(a l(alj( lj(`p `p *~ qohbf qohbf >4 LC "Quaao "Quaaoqq( qq(" "
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Alh Alhstgup stgupf² f² a˕ fl
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† Moqf}kyf²a˕ afl f˕l mf fu}oh}kaf²a˕ afl f˕l mo alhor˕ loq loq EJ]^3 loq loq hl qopyk²al al EJ]^ oj vufevuop kh}opifao3 † Faok}fp alhor˕ loq loq hl qopyk²al al QKOYO oj vufevuop kh}opifao3 † Faok}fp alhor˕ 6 0 1 = ? 9 7
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Oj qogukmf% moyo*qo "kk+ apkfp lq mkpo}½ lpklq hl elafe f~pl~pkfml% "kkk+ alhstgupfp fq ~opjkqq˕ lpklq loq loq ~fpf l uqu½ fpkl fpkl a{puq% al( a{puq% o "ky+ pokhkakfp l qopyk²al( ! jcmkp ,yfp,q~ll ,yfp,q~lle,a{p e,a{puq,j uq,jfke6 fke6 ,yfp,q~ll ,yfp,q~lle,a{p e,a{puq,j uq,jfke0 fke0 ! ablwh a{puq4 a{puq4 ,yfp,q~lle ,yfp,q~lle,a{pu ,a{puq,jfk q,jfke6 e6 ,yfp,q~lle ,yfp,q~lle,a{pu ,a{puq,jfk q,jfke0 e0 ! khylco*pa( khylco*pa(m m a{puq0(0 a{puq0(0 poq}fp} poq}fp}
Hoq}o jljoh}l% fq hlyfq ~fp}k²a˕ aloq l˕oq KJF^ oq}˕ fl fl mkq~lh mkq~ lh½½Ķyokq ~fpf uql% o ~lmo*qo ~ lmo*qo qlekak}fp fl qopyk² al al mo fpjftohfjoh}l mo johqfgohq vuo jlyf mo}opjkhfmfq afkrfq ~lq}fkq orkq}oh}oq ~fpf oq}fq fpofq ½ mo mkqal% alhilpjo oroj~el f qogukp4 - ha elaf elafeb eblq lq} } 6=1 6=1 Q4 $ LC wf}op wf}op A{puq A{puq KJF^= KJF^= y0(0(6 y0(0(61*M 1*Mo`k o`kfh* fh*0(0 0(0(61 (61*6; *6; qopyop qopyop pofm{ pofm{ A4 ( ELGKH ELGKH kjf~*f kjf~*fmjk mjkh h 601=?9 601=?9 Q4 ( LC _qop _qop elgg elggom om kh A4 ( POHFJO POHFJO uqop,pokN uqop,pokNoroj~ oroj~el(al el(alj(`p j(`p uqop,pokN uqop,pokNoroj~ oroj~el(al el(alj(`p j(`p oroj~el6 oroj~el6 Q4 ( LC Alj~ Alj~eo eo}o }om m A4 ( POHFJO POHFJO uqop,dlbh uqop,dlbhmloNo mloNoroj~e roj~el(al l(alj(`p j(`p uqop,dlbhm uqop,dlbhmloNor loNoroj~el oj~el(alj( (alj(`p `p oroj~el0 oroj~el0 Q4 ( LC Alj~ Alj~eo eo}o }om m
yopkstvuo vuo l afjkhbl afjkhbl mo fpjftohf fpjftohfjoh joh}l }l mo johqfgoh johqfgohq% q% pofekto pofekto f fe}opf² fe}opf² a˕fl fl mf ~fp}k²a˕ afl f˕l ]fpoif4 yopkst KJF^ alhilpjo khmkafml% o alhstpjo l hlyl elafe mf johqfgoj oj mkqal( Fl pofektfp l ~plaomkjoh}l mo apkf²a˕ a˕fl fl mo afkrfq ~lq}fkq% ~lmo*qo khmkafp f ~fp}k²a˕ a˕fl f l KJF^ fl vufe oq}f ~op}ohaop½ f% f % oj afql mo ljkqq˕fl% fl% f ~fp}k²a˕ afl f˕l KJF^ alhstgupfmf hf l~²a˕ afl f˕l moifue}~fp}k}klh qop½f u}kektfmf( ^fpf vuo f afkrf ~lq}fe qodf apkfmf mkpo}fjoh}o oj ujf mo}opjkhfmf ~fp}k²a˕ afl f˕l KJF^ ~lmo*qo u}kektfp l oroj~el f qogukp4 A4 ( APOF]O APOF]O uqop,pokh uqop,pokhfemlN femlNoroj~ oroj~el(a el(alj(` lj(`p p oroj~el6 oroj~el6 Q4 ( LC Alj~ Alj~eo eo}o }om m
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Af~½ Af~ ½Ķ}uel =( A{puq
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Fq afkrfq ~lq}fkq gel`fkq ~lmoj ~lqqukp ~opjkqq˕fl fl mo oqapk}f ~fpf mo}opjkhfmlq uqu½ fpklq% fpklq% ~op* jk}khml f oq}o uqu½fpkl f pkl f khqop²a˕ afl f˕ l o pojl²a˕ afl f˕l mo johq johqfgo fgohq( hq( ^f ^fpf pf kq}l% kq}l% u}kek u}kekto to l ~plaom ~plaomkj kjoh oh}l }l f qogukp4 - ha elaf elafeb eblq lq} } 6=1 6=1 Q4 $ LC wf}op wf}op A{puq A{puq KJF^= KJF^= y0(0(6 y0(0(61*M 1*Mo`k o`kfh* fh*0(0 0(0(61 (61*6; *6; qopyop qopyop pofm{ pofm{ A4 ( ELGKH ELGKH kjf~*f kjf~*fmjk mjkh h 601=?9 601=?9 Q4 ( LC _qop _qop elgg elggom om kh A4 ( QO]FAE QO]FAE fykqlqNor fykqlqNoroj~el oj~el(alj( (alj(`p `p pokNoroj~e pokNoroj~el(al l(alj(`p j(`p epqwk~am epqwk~am Q4 ( LC Alj~ Alj~eo eo}o }om m
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9(0
Kh}o Kh }ogp gpf f²a˕ a˕ fl fl alj alj L~ L~oh ohEm Emf~ f~
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† ,o}a,~lq}str,jfkh(ai 6 0 1 = ? 9 7 2 ; 6>
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