Counting the number of solutions to the Erdos-Straus equation on unit fractions

Christian Elsholtz, Terence Tao

For any positive integer $n$, let $f(n)$ denote the number of solutions to the Diophantine equation $\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ with $x,y,z$ positive in…