IMO 2009 Shortlist N3
Let f be a non-constant function from the set of positive integers into the set of positive integers, such that a − b di...
Category: Number Theory
Problem
Let f be a non-constant function from the set of positive integers into the set of positive integers, such that a − b divides f(a) − f(b) for all distinct positive integers a,b. Prove that there exist infinitely many primes p such that p divides f(c) for some positive integer c.