PROOF OF SOME CONJECTURAL CONGRUENCES OF DA SILVA AND SELLERS

Abstract Let $p_{\{3, 3\}}(n)$ denote the number of $3$ -regular partitions in three colours. Da Silva and Sellers [‘Arithmetic properties 3-regular colours’, Bull. Aust. Math. Soc. 104 (3) (2021), 415–423] conjectured four Ramanujan-like congruences modulo $5$ satisfied by . We confirm these conjectural using theory modular forms.