## IMO 2011 (Problem 5)

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 $m$ and $n$ with $f(m)\leq f(n)$ , the number $f(n)$ is divisible by $f(m)$ .