Problem

Source: 2019 Saudi Arabia IMO TST I p2 - variation of 2018 Shortlist N1

Tags: number theory, Divisors



Find all pair of integers $(m,n)$ and $m \ge n$ such that there exist a positive integer $s$ and a) Product of all divisor of $sm, sn$ are equal. b) Number of divisors of $sm,sn$ are equal.