General Solution of the Diophantine equation involving Mersenne Prime

2023/07/14 by Ghosh, Arkabrata
#11A41 #11D61 #11D72 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2307.07161

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.

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