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product or number of all divisor of $sm, sn are equal

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

July 28, 2020

number theoryDivisors

Problem Statement

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.