Primes of the form $x^2+dy^2$ with $x\equiv 0\pmod{N}$ or $y\equiv 0\pmod{N}$

Abstract

In this paper we charatcterize primes of the form $x^2+dy^2$ with $x\equiv 0\pmod{N}$ or $y\equiv 0\pmod{N}$ for positive integer $N$ and $d$ with $d$ being square free.