MathNet 2023-part-04 — 191 problems (EN–VI) Question 40

Let $n, m \ge 3$ be odd numbers. A sequence of $mn-1$ positive integers is written on a circle in such a way that the sum of any $m$ consecutive integers is a power of $m$. Show that the sequence contains a term which is repeated at least $m+1$ times.
(Bayarmagnai Gombodorj)