Distribution of the k-regular partition function modulo composite integers M

Yiwen Lu; Xuejun Guo

paper

Distribution of the k-regular partition function modulo composite integers M

arXiv:2212.05013

Abstract

Let $b_{k} (n)$ denote the $k -$ regular partitons of a natural number $n$ . In this paper, we study the behavior of $b_{k} (n)$ modulo composite integers $M$ which are coprime to $6$ . Specially, we prove that for arbitrary $k -$ regular partiton function $b_{k} (n)$ and integer $M$ coprime to $6$ , there are infinitely many Ramanujan-type congruences of $b_{k} (n)$ modulo $M$ .