On the Exponential Diophantine Equation $ (M_{pq} )^x+(M_{pq}+1)^y=z^2$

Authors

  • Azizul Hoque Gauhati University

Abstract

In this paper, we consider the number $M_{pq}=p^q-1$, where $p>0$ and $q>1$ are integers, and the Exponential Diophantine equation $(M_{pq} )^x +(M_{pq}+1)^y = z^2$, where $x,\ y$ and $z$ are positive integers. We find the solutions to the title equation expect the case only when both $p$ and $y$ are odd integers.

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Published

2016-04-30

Issue

Vol. 9 No. 2: (April 2016)

Section

Number Theory

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How to Cite

On the Exponential Diophantine Equation $ (M_{pq} )^x+(M_{pq}+1)^y=z^2$. (2016). European Journal of Pure and Applied Mathematics, 9(2), 240-243. https://www.ejpam.com/index.php/ejpam/article/view/2333