Question 29
Find all pairs $(p, q)$ of prime numbers with $p\gt q$ 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.
$$
\frac{(p+q)^{p+q}(p-q)^{p-q}-1}{(p+q)^{p-q}(p-q)^{p+q}-1}
$$
is an integer.
IMO 2017 — Complete Shortlist Question 29
IMO Shortlist · IMO 2017 — Complete Shortlist