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发表于 2016-11-2 21:34:56 | 显示全部楼层 |阅读模式
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
发表于 2016-11-3 09:27:13 | 显示全部楼层
不知道楼主链接下面给的解答是不是对的。
发表于 2016-11-7 22:05:42 | 显示全部楼层
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。
发表于 2017-1-25 13:03:24 | 显示全部楼层
反对票不少,but not [on hold].
发表于 2017-1-25 17:35:16 | 显示全部楼层
怎么还有人做Goldbach…………
发表于 2017-2-13 21:47:26 | 显示全部楼层
MO is not going to close it.
发表于 2017-5-4 22:05:09 | 显示全部楼层
@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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