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geometric mean of any subset is integer Puerto Rico TST 2007.6

Source:

September 15, 2021
geometric meanalgebra

Problem Statement

The geometric mean of a set of mm non-negative numbers is the mm-th root of the product of these numbers. For which positive values of ​​nn, is there a finite set SnS_n of nn positive integers different such that the geometric mean of any subset of SnS_n is an integer?
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