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...
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.