IMO 2024 Shortlist A5

Find all periodic sequences a1, a2, ... of real numbers such that the following conditions hold for all n ě 1: an2 a2 n ...

IMO 2024 Shortlist A5

Category: Algebra

Problem

Find all periodic sequences a1, a2, ... of real numbers such that the following conditions hold for all n ě 1: an2 a2 n “ an a2 n1 and |an`1 ´ an| ď 1. (Kosovo)