A solution to the Straus-Erd\H{o}s conjecture

TL;DR

This paper claims to have solved the Straus-Erdős conjecture by proving that for every prime p, there exist positive integers x, y, z satisfying 4/p = 1/x + 1/y + 1/z.

Contribution

The paper provides a proof confirming the existence of such integers for all primes, resolving a long-standing conjecture in number theory.

Findings

Confirmed the conjecture for all primes

Established a constructive method for x, y, z

Advanced understanding of Egyptian fraction representations

Abstract

This paper outlines a solution to the Straus Erd\H{o}s Conjecture. Namely for each prime $p$ there exists positive integers $x \leq y \leq z$ so that $$ \frac{4}{p} = \frac{1}{x}+\frac{1}{y}+\frac{1}{z} $$