Question 9
Find all quadruples $ (p, q, r, n) $ of positive integers satisfying the following three conditions:
- $p$ and $q$ are prime,
- $p+q$ is not divisible by $3$,
- $p+q = r (p-q)^n$.
- $p$ and $q$ are prime,
- $p+q$ is not divisible by $3$,
- $p+q = r (p-q)^n$.