IMO 2021 Shortlist N7

Let a1,a2,a3,... be an infinite sequence of positive integers such that an2m divides an anm for allpositive integers n a...

IMO 2021 Shortlist N7

Category: Number Theory

Problem

Let a1,a2,a3,... be an infinite sequence of positive integers such that an2m divides an anm for allpositive integers n and m. Prove that this sequence is eventually periodic, i.e. there exist positive integers N and d such that an “and for all n ąN.