On the Erdos-Straus conjecture

TL;DR

This paper extends Mordell's theorem related to the Erdos-Straus conjecture and proposes a stronger conjecture, advancing understanding of Egyptian fraction representations for rational numbers.

Contribution

It proves an extension of Mordell's theorem and introduces a new, stronger conjecture related to the Erdos-Straus problem.

Findings

Extended Mordell's theorem

Formulated a stronger conjecture than Erdos'

Provides new insights into Egyptian fractions

Abstract

Paul Erdos conjectured that for every n in N, n>1, there exist a, b, c natural numbers, not necessarily distinct, so that 4/n=1/a+1/b+1/c (see \cite{rg}). In this paper we prove an extension of Mordell's theorem and formulate a conjecture which is stronger than Erdos' conjecture.