On 2-color partitions where one of the color is multiples of $5^k$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916651454169088 |
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| author | C., Shivashankar B., HemanthKumar Gireesh, D. S. |
| author_facet | C., Shivashankar B., HemanthKumar Gireesh, D. S. |
| contents | In this work, we investigate the arithmetic properties of $p_{1,5^k}(n)$, which counts 2-color partitions of $n$ where one of the colors appears only in parts that are multiples of $5^k$. By constructing generating functions for $p_{1,5^k}(n)$ across specific arithmetic progressions, we establish a set of Ramanujan-type infinite family of congruences modulo powers of $5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10113 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On 2-color partitions where one of the color is multiples of $5^k$ C., Shivashankar B., HemanthKumar Gireesh, D. S. Number Theory In this work, we investigate the arithmetic properties of $p_{1,5^k}(n)$, which counts 2-color partitions of $n$ where one of the colors appears only in parts that are multiples of $5^k$. By constructing generating functions for $p_{1,5^k}(n)$ across specific arithmetic progressions, we establish a set of Ramanujan-type infinite family of congruences modulo powers of $5$. |
| title | On 2-color partitions where one of the color is multiples of $5^k$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.10113 |