Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.0 AIME, harder Prove it Belarus

Find the least positive integer $n$ for which there exists a set $\{s_1, \dots, s_n\}$ consisting of $n$ distinct positive integers such that
$\left(1 - \frac{1}{s_1}\right) \left(1 - \frac{1}{s_2}\right) \cdots \left(1 - \frac{1}{s_n}\right) = \frac{51}{2010}$
(IMO-2010 Shortlist, Problem N1)

Solution

2. See IMO-2010 Shortlist, Problem N1.

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