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PROOF OF SOME CONJECTURAL CONGRUENCES OF DA SILVA AND SELLERS
Published online by Cambridge University Press: 13 December 2021
Abstract
Let $p_{\{3, 3\}}(n)$ denote the number of $3$ -regular partitions in three colours. Da Silva and Sellers [‘Arithmetic properties of 3-regular partitions in three colours’, Bull. Aust. Math. Soc. 104(3) (2021), 415–423] conjectured four Ramanujan-like congruences modulo $5$ satisfied by $p_{\{3, 3\}}(n)$ . We confirm these conjectural congruences using the theory of modular forms.
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- Research Article
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- © The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
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