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Congruences of $\ell$− Regular Partition Triples for $\ell\in \{2, 3, 4, 5\}$
Nipen Saikia
,
Chayanika Boruah
Abstract
For any positive integer $\ell$, let $B_{\ell}(n)$ denotes the number of $\ell$-regular partition triples of a positive integer $n$. By employing $q$−series identities, we prove infinite family of arithmetic identities and congruences modulo 4 for $B_2(n)$, modulo 2 and 9 for $B_3(n)$, modulo 2 for $B_4(n)$ and modulo 2 and 5 for $B_5(n)$.