IMO 2015 Shortlist N7

Let Zą0 denote the set of positive integers. For any positive integer k, a function f : Zą0 Ñ Zą0 is called k-good if gc...

IMO 2015 Shortlist N7

Category: Number Theory

Problem

Let Zą0 denote the set of positive integers. For any positive integer k, a function f : Zą0 Ñ Zą0 is called k-good if gcd fpmq n,fpnq ` m ˘ ď k for all m ‰ n. Find all k such that there exists a k-good function. (Canada)