Title: Characterizing the number of coloured $m$-ary partitions modulo $m$, with and without gaps,
Abstract: In a pair of recent papers, Andrews, Fraenkel and Sellers provide a complete
characterization for the number of $m$-ary partitions modulo $m$, with and
without gaps. In this paper we extend these results to the case of coloured
$m$-ary partitions, with and without gaps. Our method of proof is different,
giving explicit expansions for the generating functions modulo $m$