Research Article

Congruences modulo powers of 5 for 5 ^k -regular bipartitions

Published in: Quaestiones Mathematicae
Volume 49 , issue 3 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 387–397

DOI: 10.2989/16073606.2025.2590576

Author(s): Zhuohang Chen Chongqing Normal University, P.R. China, Dazhao Tang Chongqing Normal University, P.R. China,

Keywords: 11P83, 05A17, 05A15, Partitions, congruences, ℓ-regular bipartitions, generating functions,

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Abstract

Let B _ℓ(n) denote the number of ℓ-regular bipartitions of n. In this paper, we investigate congruence properties of B _5k(n) modulo high powers of 5. By deriving the exact generating functions of specific arithmetic progressions in B _5k(n), we prove an extensive family of congruences modulo high powers of 5. This significantly extends the previous results of L. Wang (Ramanujan J. 44(3) (2017), 471–491) and D. Ranganatha (Indian J. Pure Appl. Math. 48(3) (2017), 449–465).

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