Arya Bhatta Journal of Mathematics and Informatics

  • Year: 2025
  • Volume: 17
  • Issue: 1

Integral Solutions of the Homogeneous Quinary Quintic Diophantine Equation Involving Palindrome Number p5 + q5 − p2q2 (p + q) = 939 (p + q)(r − s)2t2

1Assistant Professor, PG and Research Department of Mathematics, Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Trichy-18, (Tamil Nadu)

2Associate Professor, PG and Research Department of Mathematics, Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Trichy-18, (Tamil Nadu)

3PG Scholar, Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Trichy-18, (Tamil Nadu) India

Abstract

The study focuses on a homogeneous quinary quintic equation, represented asp5 + q5 − p2q2 (p + q) = 939 (p + q)(r − s)2t2 involving palindrome number. It explores various patterns of integral solutions that satisfy the equation as well as distinct non-zero integer solutions. The study also identifies some special numbers and a few interesting relationships between the solutions.

Keywords

Homogeneous quinary quintic diophantine equation, Integral solutions, Palindrome numbers