A short proof of the conjecture of Erdös--Straus for every $n\equiv 13\text{ mod }24$

Abstract

The Erdös--Straus conjecture states that the equation $\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ has positive integer solutions $x,y,z$ for every postive integers $n\ge 2$. In this short note we find explicity the solutions of the famous conjecture for the case $n\equiv 13\text{ mod }24.$

arXiv comment6 pages, J. Interdiscip. Math published on line 23 June 2021, In press

References in corpus (2)

• The Erdős-Straus conjecture New modular equations and checking up to $N=10^{17}$
• Solutions to Diophantine Equation of Erdos-Straus Conjecture