I am not able to solve this equation. Can anybody help?
$p$, $q$ are prime numbers and $a$ is a positive integer.
$$ \frac{pq}{p+q}=\frac{a^2+1}{a+1} $$
The task is to find ALL possible pairs of $p,q$ for this equation.
I've already rewritten that as:
$$ p \cdot q \cdot a - p \cdot a^2 - q \cdot a^2 = -p \cdot q + p + q $$
and I found that one solution is $\{p=2,q=2,a=1\}$.