Some new congruences for $(7,t)$-regular bipartitions modulo $t$

T. Kathiravan K. Srilakshmi

Published 2019-08-19Version 1

In this work, we study the function $B_{s,t}(n)$, which counts the number of $(s,t)$-regular bipartitions of $n$. Recently, many authors proved infinite families of congruences modulo $11$ for $B_{3,11}(n)$, modulo $3$ for $B_{3,s}(n)$ and modulo $5$ for $B_{5,s}(n)$. Very recently, Kathiravan proved several infinite families of congruences modulo $11$, $13$ and $11$ for $B_{5,11}(n)$, $B_{5,13}(n)$ and $B_{2,8}(n)$. In this paper, we will prove infinite families of congruences modulo $5$ for $B_{2,15}(n)$, modulo $11$ for $B_{7,11}(n)$ and modulo $13$ for $B_{7,13}(n)$.