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Partition of set with equal sums

Source: India Postal Set 4 P4

January 18, 2017
number theorycombinatorics

Problem Statement

Let n∈Nn \in \mathbb N. Prove that for each factor m \ge n of n(n+1)/2n(n + 1)/2, one can partition the set {1,2,3,⋯ ,n}\{1,2, 3,\cdots , n\} into disjoint subsets such that the sum of elements in each subset is equal to mm.
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