Divisibility and distribution of 5-regular partitions

Abstract

In this paper we study $b_5(n)$, the $5$-regular partitions of $n$. Using the theory of modular forms, we prove several theorems on the divisibility and distribution properties of $b_5(n)$ modulo prime $m\ge 5$. In particular, we prove that there are infinitely many Ramanujan-type congruences modulo prime $m\ge 5$.

arXiv comment7 pages. arXiv admin note: text overlap with arXiv:2205.03191