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ON
$5^k$-REGULAR PARTITIONS MODULO POWERS OF 
$5$
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 14 April 2025, pp. 1-9
-
- Article
- Export citation
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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.
