Let be a function from the set of integers to the set of positive integers. Suppose that, for any two integers and , the difference is divisible by Prove that, for all integers and with , the number is divisible by .

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- Jul 19th 2011, 10:06 AMFernandoRevillaIMO 2011 (Problem 5)
Let be a function from the set of integers to the set of positive integers. Suppose that, for any two integers and , the difference is divisible by Prove that, for all integers and with , the number is divisible by .