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Partition into equal-element sets with divisibility condition

Source: 3rd Memorial Mathematical Competition "Aleksandar Blazhevski - Cane"- Junior D2 P4

January 17, 2022
number theorySetsdisjoint subsetsDivisibility

Problem Statement

Find all positive integers nn such that the set S={1,2,3,…2n}S=\{1,2,3, \dots 2n\} can be divided into 22 disjoint subsets S1S_1 and S2S_2, i.e. S1∩S2=∅S_1 \cap S_2 = \emptyset and S1∪S2=SS_1 \cup S_2 = S, such that each one of them has nn elements, and the sum of the elements of S1S_1 is divisible by the sum of the elements in S2S_2.
Proposed by Viktor Simjanoski
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