MathDB

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

S_n

n

distinct positive integers such that the geometric mean of any subset of

S_n

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?

Problem Statement