A quartic diophantine equation inspired by Brahmagupta's identity

TL;DR

This paper derives parametric solutions for a specific quartic Diophantine equation inspired by Brahmagupta's identity, utilizing elliptic curves to generate infinitely many solutions.

Contribution

It introduces a method to find parametric solutions to a quartic Diophantine equation using elliptic curves, expanding the understanding of such equations.

Findings

Multiple parametric solutions derived

Infinite solutions generated via elliptic curves

Connection to Brahmagupta's identity established

Abstract

In this paper we obtain several parametric solutions of the quartic diophantine equation $(x_1^4+x_2^4)(y_1^4+y_2^4)=z_1^4+z_2^4$. We also show how infinitely many parametric solutions of this equation may be obtained by using elliptic curves.