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

Mario Gionfriddo, Elena Guardo

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 $n\ge 2$.…