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

Authors

  • Kalyan Chakraborty SRM University AP
  • Azizul Hoque Harish-Chandra Research Institute

DOI:

https://doi.org/10.53733/345

Keywords:

Exponential Diophantine equation, Lehmer number, Primitive divisor

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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Author Biographies

Kalyan Chakraborty, SRM University AP

Kalyan Chakraborty
Department of Mathematics
SRM University AP
Neerukonda, Mangalagiri Mandal
Guntur-522240
Andhra Pradesh,
India.
kalyan.c@srmap.edu.in

Azizul Hoque, Harish-Chandra Research Institute

Azizul Hoque
Department of Mathematics,
Faculty of Science, Rangapara College,
Rangapara, Sonitpur-784505,
Assam,
India
ahoque.ms@gmail.com

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Published

23-07-2024

How to Cite

Chakraborty, K., & Hoque, A. (2024). On the exponential Diophantine equation $x^2+p^mq^n=2y^p$. New Zealand Journal of Mathematics, 55, 53–60. https://doi.org/10.53733/345

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Section

Articles