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

Kalyan Chakraborty; Azizul Hoque

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

Number Theory 2023-08-25 v1

Authors: Kalyan Chakraborty , Azizul Hoque

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.

Keywords

exponential diophantine equation lehmer sequences primitive divisors odd primes solvability elementary number theory

Cite

@article{arxiv.2308.12708,
  title  = {On the exponential Diophantine equation $x^2+p^mq^n=2y^p$},
  author = {Kalyan Chakraborty and Azizul Hoque},
  journal= {arXiv preprint arXiv:2308.12708},
  year   = {2023}
}

Comments

10 pages. To appear in `New Zealand J. Math.'

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