On the exponential Diophantine equation $x^2+p^mq^n=2y^p$

Kalyan Chakraborty; Azizul Hoque

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arXiv · 2308.12708

On the exponential Diophantine equation $x^2+p^mq^n=2y^p$

Kalyan Chakraborty·Azizul Hoque

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Abstract

We study the exponential Diophantine equation $x^2+p^mq^n=2y^p$ in positive integers $x,y,m,n$, and odd primes $p$ and $q$ using primitive divisors of Lehmer sequences in combination with elementary number theory. We discuss the solvability of this equation.

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Kalyan Chakraborty, Azizul Hoque. 2023-08-24. On the exponential Diophantine equation $x^2+p^mq^n=2y^p$. https://arxiv.org/abs/2308.12708

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