Question 93
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.
MathNet 2017-part-03 — 176 problems (EN–VI) Question 93
Math Olympiad Vault · MathNet 2017-part-03 — 176 problems (EN–VI)