MathDB

N5

Part of 2017 IMO Shortlist

Problems(1)

Weird expression being integer.

Source: IMO Shortlist 2017 N5

7/10/2018
Find all pairs (p,q)(p,q) of prime numbers which p>qp>q and (p+q)p+q(p−q)p−q−1(p+q)p−q(p−q)p+q−1\frac{(p+q)^{p+q}(p-q)^{p-q}-1}{(p+q)^{p-q}(p-q)^{p+q}-1} is an integer.
number theoryIMO Shortlist