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Unformatted text preview: p~oo p pd =-- -- I(N} In particular, for all sufficiently large p with p A - - 1 mod (N), we have (184.108.40.206) 1__ Rv ( _b)> 1__ R~,(-c). P P As this is incompatible with (220.127.116.11), (18.104.22.168) holds for such p, and in particular, (6.6.0) gives (22.214.171.124) 1Rp(-c)>__l Rp(-a). Substituting via (126.96.36.199), this gives (188.8.131.52) (_cA)__c_>__(_aA) a P P As c-aeZ, (-cA)=(-aA), hence --r --a (184.108.40.206) --=>_ , P P which contradicts (220.127.116.11), and concludes the proof that c-aCZ. By symmetry we conclude that c-bCZ....
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- Fall '11