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...
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)