MathDB

Weird expression being integer.

Source: IMO Shortlist 2017 N5

July 10, 2018

number theoryIMO Shortlist

Problem Statement

Find all pairs

(p,q)

of prime numbers which

p>q

and

\frac{(p+q)^{p+q}(p-q)^{p-q}-1}{(p+q)^{p-q}(p-q)^{p+q}-1}

is an integer.