MathDB
IMO Shortlist 2010 - Problem N1

Source:

July 17, 2011
number theoryequationIMO Shortlistnumber theory solvedmultiplication

Problem Statement

Find the least positive integer nn for which there exists a set {s1,s2,…,sn}\{s_1, s_2, \ldots , s_n\} consisting of nn distinct positive integers such that (1−1s1)(1−1s2)⋯(1−1sn)=512010. \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
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