• Primes of the form $x^2+dy^2$ with $x\equiv 0({\rm mod}\, N)$ or $y\equiv 0({\rm mod}\, N)$

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/127/01/0035-0043

• # Keywords

Artin reciprocity; cyclic quartic unramified extension; Gaussian-Mersenne prime; Eisenstein-Mersenne prime.

• # Abstract

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

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019