General Solution of the Diophantine equation involving Mersenne Prime

Arkabrata Ghosh

paper

General Solution of the Diophantine equation involving Mersenne Prime

arXiv:2307.07161

Abstract

In this article, I study and solve the exponential Diophantine equation $M_{p}^{x} + (M_{q} + 1)^{y} = (l z)^{2}$ where $M_{p}$ and $M_{q}$ are Mersenne primes, $l$ is a prime number, and $x, y$ , and $z$ are non-negative integers. Several illustrations are presented as well as cases where no solution of the given Diophantine equation is present.

7 Pages