Find the least positive integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
for which there exists a set
![\{s_1, s_2, \ldots , s_n\}](/media/m/9/a/6/9a67aea2351075523cbc461ed1394eb2.png)
consisting of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
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}.](/media/m/c/b/3/cb3100eb354741fe9ab9f8db005bd910.png)
Proposed by Daniel Brown, Canada
%V0
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