Some New Congruences Modulo 5 for the General Partition Function

In the present work, we discover some new congruences modulo 5 for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p_r(n)$\end{document}, 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p_r(n)$\end{document}.