Inspired by Romain Bouchard

Algebra Level 3

Let \(a_1,a_2,...,a_n\) be distinct positive integers such that \(a_1+a_2+\cdots+a_n=2018.\)

Find the maximum value of \(a_1\times a_2\times \cdots \times a_n.\)

If this is equal to \(\frac{a!}{b}\), where \(a\) and \(b\) are distinct positive integers and \(a+b\) is minimized, write your answer as \(\frac{ab}{2}.\)

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