Prove that $a|p+1$ if and only if ${\frac{a}{p} = \frac{1}{n} + \frac{1}{m} }$ such that $n,m \in N$ and $p$ is prime
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$