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ASU 482 All Soviet Union MO 1988 1+2+... +n = mk, k groups division

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August 8, 2019
combinatoricsSumalgebra

Problem Statement

Let m,n,km, n, k be positive integers with m≥nm \ge n and 1+2+...+n=mk1 + 2 + ... + n = mk. Prove that the numbers 1,2,...,n1, 2, ... , n can be divided into kk groups in such a way that the sum of the numbers in each group equals mm.
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