2014-08 Two positive integers

Let \(a\), \(b\) be distinct positive integers. Prove that there exists a prime \(p\) such that when dividing both \(a\) and \(b\) by \(p\), the remainder of \(a\) is less than the remainder of \(b\).

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2014-08 Two positive integers, 3.4 out of 5 based on 7 ratings