2021/10/27 by Ajit Singh, Singh, Ajit, Rupam Barman +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2110.14159
openalex publication_date 2021/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.