Two congruences involving Andrews-Paule's broken 3-diamond partitions and 5-diamond partitions

TL;DR

This paper proves two conjectured congruences related to broken 3-diamond and 5-diamond partitions, advancing understanding of their modular properties.

Contribution

It provides rigorous proofs for two previously conjectured congruences involving broken diamond partitions.

Findings

Confirmed congruences for broken 3-diamond partitions

Confirmed congruences for broken 5-diamond partitions

Enhanced knowledge of partition congruences

Abstract

In this note, we will give proofs of two congruences involving broken 3-diamond partitions and broken 5-diamond partitions which were conjectured by Peter Paule and Silviu Radu.