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partition set of n elements in m sets with same sum of elements, criterion

Source: Danube 2012 p4

July 22, 2019
combinatoricsSumSubsetssetdivisor

Problem Statement

Given a positive integer nn, show that the set {1,2,...,n}\{1,2,...,n\} can be partitioned into mm sets, each with the same sum, if and only if m is a divisor of n(n+1)2\frac{n(n + 1)}{2} which does not exceed n+12\frac{n + 1}{2}.
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