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Unformatted text preview: either (220.127.116.11) l > (b A) > (cA)=(aA) >O Or" (18.104.22.168) 1 > (aA) = (cA) > (bA) >0. But (22.214.171.124) cannot hold for both A and -A. Hence there exists a A invertible modulo N for which (126.96.36.199) holds. Rewriting (188.8.131.52) for this A via the limit formula (184.108.40.206), we get (220.127.116.11) 1> lim 1Rp(-a)= lim LRp(--c)> lim 1---Rp(-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 (18.104.22.168) 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) (22.214.171.124) l~ Rv(-b)>lRp(-c)>lRp(-a), P P P (126.96.36.199) 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