Four squares from three numbers

TL;DR

This paper proves the existence of infinitely many triples of positive integers greater than 1 where specific products plus one are perfect squares, revealing a new infinite family of such number triples.

Contribution

It establishes the infinite existence of triples with all six related expressions being perfect squares, a novel result in number theory.

Findings

Infinitely many such triples exist.

All related expressions are perfect squares.

The result expands understanding of special number triples.

Abstract

We show that there are infinitely many triples of positive integers a, b, c (greater than 1) such that ab + 1, ac + 1, bc + 1 and abc + 1 are all perfect squares.