GM of set = GM of the GMs of all non-zero subsets
Source: Canadian Mathematical Olympiad - 1983 - Problem 5.
June 26, 2011
combinatorics proposedcombinatorics
Problem Statement
The geometric mean (G.M.) of positive integers , , , is defined to be the (positive) -th root of their product. For example, the G.M. of 3, 4, 18 is 6. Show that the G.M. of a set of positive numbers is equal to the G.M. of the G.M.'s of all non-empty subsets of .