Unformatted text preview: either (18.104.22.168) l > (b A) > (cA)=(aA) >O Or" (22.214.171.124) 1 > (aA) = (cA) > (bA) >0. But (126.96.36.199) cannot hold for both A and -A. Hence there exists a A invertible modulo N for which (188.8.131.52) holds. Rewriting (184.108.40.206) for this A via the limit formula (220.127.116.11), we get (18.104.22.168) 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 (22.214.171.124) 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) (126.96.36.199) l~ Rv(-b)>lRp(-c)>lRp(-a), P P P (188.8.131.52) 1Rp(-a)> l~ Rp(-C)>__lRp(-b). P P P...
View Full Document
- Fall '11
- Trigraph, 184.108.40.206, 220.127.116.11, 18.104.22.168, 22.214.171.124