Question 53
The numbers $p$ and $q$ are prime and satisfy
$$
\frac{p}{p+1}+\frac{q+1}{q}=\frac{2 n}{n+2}
$$
for some positive integer $n$. Find all possible values of $q-p$.
$$
\frac{p}{p+1}+\frac{q+1}{q}=\frac{2 n}{n+2}
$$
for some positive integer $n$. Find all possible values of $q-p$.