The number of cubic partitions modulo powers of 5

TL;DR

This paper investigates the properties of cubic partition functions, establishing Ramanujan-type congruences modulo powers of 5, extending previous work on their congruences modulo 3 and 5.

Contribution

It provides new Ramanujan-type congruences for cubic partition functions modulo powers of 5, expanding understanding of their modular properties.

Findings

Established Ramanujan-type congruences modulo powers of 5

Extended previous results on cubic partition congruences

Contributed to the theory of partition functions and modular forms

Abstract

The notion of cubic partitions is introduced by Hei-Chi Chan and named by Byungchan Kim in connection with Ramanujan's cubic continued fractions. Chan proved that cubic partition function has Ramanujan Type congruences modulo powers of $3$. In a recent paper, William Y.C. Chen and Bernard L.S. Lin studied the congruent property of the cubic partition function modulo $5$. In this note, we give Ramanujan type congruences for cubic partition function modulo powers of $5$.