Treffer: Congruences modulo powers of 5 for 5<italic>k</italic> -regular bipartitions.

Title:
Congruences modulo powers of 5 for 5k -regular bipartitions.
Authors:
Chen, Zhuohang1 (AUTHOR) yychen1226@163.com, Tang, Dazhao1 (AUTHOR) dazhaotang@sina.com
Source:
QM - Quaestiones Mathematicae. Nov2025, p1-11. 11p.
Subject Terms:
*MODULAR arithmetic, *GENERATING functions, *NUMBER theory, *PARTITIONS (Mathematics), *CONGRUENCE lattices, *MATHEMATICAL sequences
Database:
Academic Search Index

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