Primes of the form $x^2+d{y}^2$ with $x\equiv 0(\mathrm{mod}N)$ or $y\equiv 0(\mathrm{mod}N)$

Abstract

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

arXiv commentarXiv admin note: substantial text overlap with arXiv:1401.6656

References in corpus (2)

• Mersenne Primes in Real Quadratic Fields
• Gaussian Mersenne Primes of the form $x^2+d{y}^2$