IMO 2011 (Problem 5)

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• July 19th 2011, 10:06 AM
FernandoRevilla
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 $f(m)$ .