IMO 2024 Shortlist C7
Let N be a positive integer and let a1, a2, ... be an infinite sequence of positive integers. Suppose that, for each n ą...
Category: Combinatorics
Problem
Let N be a positive integer and let a1, a2, ... be an infinite sequence of positive integers. Suppose that, for each n ą N, an is equal to the number of times an´1 appears in the list a1, a2, ..., an´1. Prove that at least one of the sequences a1, a3, a5, ... and a2, a4, a6, ... is eventually periodic. (Australia)