On the Enumeration and Congruences for m-ary Partitions

Lisa Hui Sun, Mingzhi Zhang

Let $m\ge 2$ be a fixed positive integer. Suppose that $m^j\le n<m^{j+1}$ is a positive integer for some $j\ge 0$. Denote $b_m(n)$ the number of $m$-ary partitions of $n$, whe…