2018-08 Large LCM

Let \(a_1\), \(a_2\), \(\ldots\), \(a_m\) be distinct positive integers. Prove that if \(m>2\sqrt{N}\), then there exist \(i\), \(j\) such that the least common multiple of \(a_i\) and \(a_j\) is greater than \(N\).

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2018-08 Large LCM, 3.8 out of 5 based on 10 ratings