IMO 2018 Shortlist N4
Let a1, a2, ..., an, ... be a sequen e of positive integers su h that a1 a2 a2 a3 ¨¨¨ an´1 an an a1 is an integer for al...
Category: Number Theory
Problem
Let a1, a2, ..., an, ... be a sequen e of positive integers su h that
a1
a2
a2 a3 ¨¨¨ an´1 an
an
a1
is an integer for all n ě k, where k is some positive integer. Prove that there exists a positive
integer m su h that an “ an`1 for all n ě m.
(Mongolia)