Abstract:
In the present work, we discover some new congruences modulo $5$ for $p_r(n)$, the general partition function by restricting $r$ to some sequence of negative integers. Our emphasis throughout this paper is to exhibit the use of $q$-identities to generate the congruences for $p_r(n)$.
Keywords:$q$-identity, Partition congruence, Ramanujan's general partition function.