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ON $5^k$-REGULAR PARTITIONS MODULO POWERS OF $5$

Part of: Combinatorics Additive number theory; partitions

Published online by Cambridge University Press:  14 April 2025

B. HEMANTHKUMAR Open the ORCID record for B. HEMANTHKUMAR [Opens in a new window]  and
D. S. GIREESH Open the ORCID record for D. S. GIREESH [Opens in a new window]
B. HEMANTHKUMAR
Affiliation:
Department of Mathematics, RV College of Engineering, RV Vidyanikethan Post, Mysore Road, Bengaluru 560 059, Karnataka, India e-mail: hemanthkumarb.30@gmail.com
D. S. GIREESH*
Affiliation:
Department of Mathematics, BMS College of Engineering, P.O. Box No. 1908, Bull Temple Road, Bengaluru 560 019, Karnataka, India
*
e-mail: gireeshdap@gmail.com
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Abstract

In this work, we investigate the arithmetic properties of $b_{5^k}(n)$, which counts the partitions of n where no part is divisible by $5^k$. By constructing generating functions for $b_{5^k}(n)$ across specific arithmetic progressions, we establish a set of Ramanujan-type congruences.

Keywords

partitionsℓ-regular partitionsgenerating functionscongruences

MSC classification

Primary: 11P83: Partitions; congruences and congruential restrictions
Secondary: 05A15: Exact enumeration problems, generating functions 05A17: Partitions of integers

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 9
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

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