IMO Shortlist 2010 problem N1


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23. lipnja 2013.
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Find the least positive integer n for which there exists a set \{s_1, s_2, \ldots , 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}.

Proposed by Daniel Brown, Canada
Izvor: Međunarodna matematička olimpijada, shortlist 2010