The exceptional set in a generalized Goldbach`s problem

Abstract

In this paper, we compute the size of the exceptional set in a generalized Goldbach problem and show that for a given polynomial $f(x)\in \mathbb{Z}[x]$ with a positive leading coefficient, positive integers $A$, $B$, $g$ and $0\le i,j<g$, there are infinitely many integers $n$ which satisfy $f(n)=Ap+Bq$ for some primes $p\equiv i,q\equiv j(\mathrm{mod}g)$ under a mild condition.

arXiv comment18 pages