Arya Bhatta Journal of Mathematics and Informatics
  • Year: 2025
  • Volume: 17
  • Issue: 1

Integral Solutions of Cubic Diophantine Equation with Four Unknowns x3 + y3 = 5(z + w)2(z − w)

1Associate Professor, PG and Research Department of Mathematics, Cauvery College for women (Autonomous), Trichy-18, (Tamil Nadu)

2PG Scholar, Cauvery College for Women (Autonomous), Trichy-18, (Tamil Nadu) India

*Email: janakikarun@rediffmail.com

**sadhanac1808@gmail.com

Online Published on 18 June, 2025.

Abstract

This study explores the non-trivial distinct integral solutions of a cubic Diophantine equation, specifically x3 + y3 = 5(z + w)2(z − w), across three different patterns. The research identifies unique polygonal numbers and highlights limited connections among the solutions.

Keywords

Integral solutions, Cubic Diophantine equations, Gnomonic number