  The Erd\"{o}s--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 $n\geq 2$. In this short note we
find explicity the solutions of the famous conjecture for the case $n\equiv13
\textrm{ mod } 24.$
