MathNet 1988 — Part 01 Question 35

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