Elementary proof of congruences modulo 25 for broken $k$-diamond partitions

Abstract

Let $\hat{I}{”}_k(n)$ denote the number of $k$-broken diamond partitions of $n$. Quite recently, the second author proved an infinite family of congruences modulo 25 for $\hat{I}{”}_k(n)$ with the help of modular forms. In this paper, we aim to provide an elementary proof of this result.

9 pages