On some partition functions.

Abstract

Introduction. Let $p_{\kappa}(n;a, M)$ be the number of partitions of a positive integer $n$ into positive summands of the form $(Ml\pm a)^{\kappa}(l=0,1,2,\cdots)$ , where $M,$ $a$ and $\kappa$ are integers satisfying $M\geqq 2,0<a<M,$ $(a, M)=1$ and $\kappa\geqq 1$ .