2017 IMO Shortlist N5

Find all pairs $(p, q)$ of prime numbers with $p>q$ for which the number $$\frac{(p+q)^{p+q}(p-q)^{p-q}-1}{(p+q)^{p-q}(p-q)^{p+q}-1}$$ is an integer.

查找 $p>q$ 的所有素数对 $(p, q)$，其中数字 $$\frac{(p+q)^{p+q}(p-q)^{p-q}-1}{(p+q)^{p-q}(p-q)^{p+q}-1}$$ 是整数。