Some new congruences for generalized overcubic partition function
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908280879579136 |
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| author | Paksok, Adam Saikia, Nipen |
| author_facet | Paksok, Adam Saikia, Nipen |
| contents | Amdeberhan et al. (2024) introduced the notion of a generalized overcubic partition function $\overline a_c (n)$ and proved an infinite family of congruences modulo a prime $p\ge 3$ and some Ramanujan type congruences. In this paper, we show that $\overline a_{2^λm+t}(n) \equiv \overline a_t (n) \pmod {2^{λ+1}}$, where $λ\geq1, m\geq0,$ and $t\geq1$ are integers. We also prove some new congruences modulo $8$ and $16$ for $\overline a_{2m+1}(n), \overline a_{2m+2}(n), \overline a_{8m+3}(n)$, where $m$ is any non-negative integer. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_18493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some new congruences for generalized overcubic partition function Paksok, Adam Saikia, Nipen Number Theory Amdeberhan et al. (2024) introduced the notion of a generalized overcubic partition function $\overline a_c (n)$ and proved an infinite family of congruences modulo a prime $p\ge 3$ and some Ramanujan type congruences. In this paper, we show that $\overline a_{2^λm+t}(n) \equiv \overline a_t (n) \pmod {2^{λ+1}}$, where $λ\geq1, m\geq0,$ and $t\geq1$ are integers. We also prove some new congruences modulo $8$ and $16$ for $\overline a_{2m+1}(n), \overline a_{2m+2}(n), \overline a_{8m+3}(n)$, where $m$ is any non-negative integer. |
| title | Some new congruences for generalized overcubic partition function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.18493 |