An easy way to find solutions of the Diophantine equation $A^{3}+B^{3}=C^{3}+D^{3}$

TL;DR

This paper presents a constructive parametrization method for the Diophantine equation A^3 + B^3 = C^3 + D^3 using integral binary quadratic forms, facilitating the finding of solutions.

Contribution

It introduces a new constructive approach to parametrize solutions of the equation using integral binary quadratic forms, advancing previous methods.

Findings

Provides a systematic parametrization of solutions.

Enables easier computation of solutions.

Enhances understanding of the structure of solutions.

Abstract

To give a parametrization of the Diophantine equation $A^{3}+B^{3}=C^{3}+D^{3}$ in terms of integral binary quadratic forms in a constructive way.