The geometric mean of any set of m non-negative numbers is the m-th root of their product. (\text{i}) For which positive integers n is there a finite set Sn of n distinct positive integers such that the geometric mean of any subset of Sn is an integer?
(\text{ii}) Is there an infinite set S of distinct positive integers such that the geometric mean of any finite subset of S is an integer? AMCUSA(J)MOUSAMOnumber theory unsolvednumber theory