IMO 2020 Shortlist N5
Determine all functions f defined on the set of all positive integers and taking non-negative integer values, satisfying...
Category: Number Theory
Problem
Determine all functions f defined on the set of all positive integers and taking non-negative integer values, satisfying the three conditions: piq fpnq ‰ 0 for at least one n; piiq fpxyq “ fpxq ` fpyq for every positive integers x and y; piiiq there are infinitely many positive integers n such that fpkq “ fpn ´ kq for all k ă n. (Croatia)