Partitioning set $[n]=\{1,\dots ,n\}$ into subsets of size at most $m$ such that all sums are powers of $m$

Vladimir Gurvich, Mariya Naumova

Given integers $m>1$ and $n>0$, we say that a partition of the set $[n]=\{1,\dots ,n\}$ is {\em $m$-good} if the number of elements in each part is at most $m$ and their sum…