Characterizing the number of coloured m-ary partitions modulo m, with and without gaps

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.