A Generalization of Goldbach's Conjecture(z)

 A Generalization of Goldbach's Conjecture : $2n = p+q$,$p\equiv q \equiv a \pmod{m}$ The Goldbach's conjecture is that $\forall n \in \mathbb{N}^*, \ \exists p,q \in \mathcal{P}$ such that $2n=p+q$ I wonder if there are some generalization giving more information about the congruence satisfied by $p,q$, for example Given $m ,a\in \mathbb{N},gcd(a,m)=1$ for every $n \equiv a \pmod{m}$ large enough, $\exists p,q \in \mathcal{P}$ such that $2n=p+q$ and $p\equiv q \equiv a \pmod{m}$ Is there some reference on this, and is it much harder than the original Goldbach's conjecture ? asked Oct 20 at 6:04 by peter http://mathoverflow.net/question ... quiv-q-equiv-a-pmod

点评

 不知道楼主链接下面给的解答是不是对的。

 十万年：不知道楼主链接下面给的解答是不是对的。 问题是数学家也不知道。

 反对票不少，but not [on hold].

 怎么还有人做Goldbach…………

 MO is not going to close it.

 @Terry Tao:Ben Green and Terrence Tao proved that there are arbitrary length arithmetic progressions among the primes. Does the prime number have symmetry in such arithmetic progressions?-peter

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