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Ramanujan type of congruences modulo m for (l, m)-regular bipartitions
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abstract
Let $B_{l,m}(n)$ denote the number of $(l,m)$-regular bipartitions of $n$. Recently, many authors proved several infinite families of congruences modulo $3$, $5$ and $11$ for $B_{l,m}(n)$. In this paper, using theta function identities to prove infinite families of congruences modulo $m$ for $(l,m)$-regular bipartitions, where $m\in\{7,3,11,13,17\}$.
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Some congruences for $(s,t)$-regular bipartitions modulo $t$
New infinite families of congruences modulo 5, 11, and 17 are proved for four (s,t)-regular bipartition functions.
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