2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146288I revisit an automated proof of Andrews' pentagonal number theorem found by Riese. I uncover a simple polynomial identity hidden behind his proof. I explain how to use this identity to prove Andrews' result along with a variety of new formulas of similar type. I reveal an interesting relation between the tri-pentagonal theorem and items (19), (20), (94), (98) on the celebrated Slater list. Finally, I establish a new infinite family of multiple series identities.13 pagesNumber TheoryCombinatorics33D15, 11B65text