What are some equivalent statements of (strong) Goldbach Conjecture ?
We all know that Riemann Hypothesis has some interesting equivalent statements.
My favorites are involved with Mertens function, error terms of Prime Number Theorem, and Farey sequences. Those equivalent statements do not use Riemann Zeta function directly, but provide additional insights about Riemann Hypothesis from very different angles.
What are some equivalent statements of (strong) Goldbach Conjecture ?
to shed lights on this problems from different angles ?
Best Answer
For every integer $n \geq 2$ there exist integers $k, p$ and $q$ with $0 \leq k \leq n-2$ and with $p$ and $q$ prime such that $n^2 - k^2 = pq$. (http://www.maa.org/sites/default/files/Reformulation-Gerstein20557.pdf)