Research Article

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

Published in: Quaestiones Mathematicae
Volume 49 , issue 3 , 2026 , 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

Download full text Get new issue alerts

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).

« On 2-nilpotent multiplier of Lie superalgebras

Geometry of δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds »