RU-ALLRUSSIAN 1988 Problem 20

Let m, n, k be positive integers with $\mathrm{m} \geq \mathrm{n}$ and $1 + 2 + \ldots + \mathrm{n} = \mathrm{mk}$ . Prove that the numbers 1, 2, ..., n can be divided into k groups in such a way that the sum of the numbers in each group equals m.