Number Theory


The Chinese Remainder Theorem . Goldbach's Conjecture (A) . Hardy-Littewood's Conjecture (A)

Authors: Tong Xin Ping

N = pi + (N-pi) = p+ (N-p). If p is congruent to N modulo pi, Then (N-p) is a composite integer, When i = 1, 2,..., r, if p and N are incongruent modulo pi, Then p and (N-p) are solutions of Goldbach's Conjecture (A); By Chinese Remainder Theorem we can calculate the primes and solutions of Goldbach's Conjecture (A) with different system of congruence; The (N-p) must have solution of Goldbach's Conjecture (A), The number of solutions of Goldbach's Conjecture (A) is increasing as N → ∞, and finding unknown particulars for Hardy-Littewood's Conjecture (A).

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[v1] 3 Jan 2009

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