IMO Shortlist 1989 problem 22


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2. travnja 2012.
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Prove that in the set \{1,2, \ldots, 1989\} can be expressed as the disjoint union of subsets A_i, \{i = 1,2, \ldots, 117\} such that

i.) each A_i contains 17 elements

ii.) the sum of all the elements in each A_i is the same.
Izvor: Međunarodna matematička olimpijada, shortlist 1989