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Congruences for Partition Quadruples with $t$-Cores
M. S. Mahadeva Naika
,
S. Shivaprasada Nayaka
Abstract
Let $C_t(n)$ denote the number of partition quadruples of $n$ with $t$-cores for $t = 3,5,7,25$. We establish some Ramanujan type congruences modulo $5, 7, 8$ for $C_t(n)$. For example, $n\ge 0$, we have $$\begin{array}{@{}rcl@{}} C_{5}(5n+4)&\equiv& 0\pmod{5},\\ C_{7}(7n+6)&\equiv& 0\pmod{7},\\ C_{3}(16n+14)&\equiv& 0\pmod{8}. \end{array}$$