2011 IMO Problems/Problem 5

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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) ≤ f(n), the number f(n) is divisible by f(m).

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