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arXiv · 2110.14159

Proof of some conjectural congruences of da Silva and Sellers

Ajit Singh·Rupam Barman
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Abstract

Let $p_{\{3, 3\}}(n)$ denote the number of $3$-regular partitions in three colours. In a very recent paper, da Silva and Sellers studied certain arithmetic properties of $p_{\{3, 3\}}(n)$. They further conjectured four Ramanujan-like congruences modulo $5$ satisfied by $p_{\{3, 3\}}(n)$. In this article, we confirm the conjectural congruences of da Silva and Sellers using the theory of modular forms.

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Ajit Singh, Rupam Barman. 2021-10-27. Proof of some conjectural congruences of da Silva and Sellers. https://arxiv.org/abs/2110.14159

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