Strong Eulerian triples

TL;DR

This paper proves the existence of infinitely many rational triples where specific quadratic expressions are perfect squares, addressing a classical problem related to Diophantus and Euler.

Contribution

It establishes the infinite existence of rational triples satisfying multiple quadratic square conditions, solving a variant of a historical mathematical problem.

Findings

Existence of infinitely many such triples.

Construction method for these triples.

Addresses a classical problem in number theory.

Abstract

We prove that there exist infinitely many rationals a, b and c with the property that a^2-1, b^2-1, c^2-1, ab-1, ac-1 and bc-1 are all perfect squares. This provides a solution to a variant of the problem studied by Diophantus and Euler.