IMO 2011 Shortlist N5
Let f be a function from the set of integers to the set of positive integers. Suppose that for any two integers m and n,...
Category: Number Theory
Problem
Let f be a function from the set of integers to the set of positive integers. Suppose that for any two integers m and n, the difference f(m) − f(n) is divisible by f(m − n). Prove that for all integers m, n with f(m) ≤ f(n) the number f(n) is divisible by f(m).