Infinite Families of Congruences Modulo 5 for Ramanujan's General Partition Function

Abstract

For any non-negative integer $n$ and non-zero integer $r$, let $p_r(n)$ denote Ramanujan's general partition function. By employing $q$-identities, we prove some new Ramanujan-type congruences modulo 5 for $p_r(n)$ for $r=-(5\lambda +1),-(5\lambda +3),-(5\lambda +4),-(25\lambda +1)$, $-(25\lambda +2)$, and any integer $\lambda$.

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