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Unformatted text preview: either (6.6.0.15) l > (b A) > (cA)=(aA) >O Or" (6.6.0.16) 1 > (aA) = (cA) > (bA) >0. But (6.6.0.15) cannot hold for both A and A. Hence there exists a A invertible modulo N for which (6.6.0.16) holds. Rewriting (6.6.0.1) for this A via the limit formula (6.5.3.1), we get (6.6.0.17) 1> lim 1Rp(a)= lim LRp(c)> lim 1Rp(b)>0. p~ p p~ p p~ p pd ~ (N) pA = 1 (N) pA =. 1 (N) Thus for all p sufficiently large with pA = 1 (N), we have (6.6.0.18) 1 Rp(_C)>L Rp(_b)>O" P P This is incompatible with the first of the two following inequalities, one or the other of which holds for any sufficiently large prime in virtue of (6.4.0) (6.6.0.19) l~ Rv(b)>lRp(c)>lRp(a), P P P (6.6.0.20) 1Rp(a)> l~ Rp(C)>__lRp(b). P P P...
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
 Fall '11
 NormanKatz

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