Pythagorean Triples, Bézout Coefficients and the Erdős-Straus Conjeceture

Abstract

This paper is a preliminary expository paper that outlines the relationship between solutions to the Erdős-Straus conjecture for a given prime $p$ and their corresponding Pythagorean triples. This paper also uses Bézout Coefficients to find a relationship between the solutions to the conjecture and roots of a second degree polynomial.