Question 43
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 N 1)
$$
\left(1 - \frac{1}{s_1}\right) \left(1 - \frac{1}{s_2}\right) \cdots \left(1 - \frac{1}{s_n}\right) = \frac{51}{2010}
$$
(IMO-2010 Shortlist, Problem N 1)