Let $A$ be a set of $n$ positive integers.
Source: Moldova TST 1997
August 8, 2023
Problem Statement
For every nonempty set of real numbers denote the sum of its elements. Let be a set of positive integers. Show that the set of all sums of all nonempty sets of can be partitioned in groups such that the ratio between the greatest number and the smallest number from each group is less than .