General Solution of the Diophantine equation involving Mersenne Prime

Arkabrata Ghosh

General Solution of the Diophantine equation involving Mersenne Prime

Number Theory 2023-07-25 v2

Authors: Arkabrata Ghosh

Abstract

In this article, I study and solve the exponential Diophantine equation $M_p^{x} + (M_q + 1)^{y}= (lz)^2$ 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.

Keywords

diophantine equation mersenne primes exponential equation integer solutions number theory

Cite

@article{arxiv.2307.07161,
  title  = {General Solution of the Diophantine equation involving Mersenne Prime},
  author = {Arkabrata Ghosh},
  journal= {arXiv preprint arXiv:2307.07161},
  year   = {2023}
}

Comments

7 Pages

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