$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
Let p be a prime. Consider the equation $\frac1x+\frac1y=\frac1p$. What are the solutions?