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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2504.06941 |
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| _version_ | 1866908309825519616 |
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| author | Chen, Jiayu Jin, Jing Yao, Olivia X. M. |
| author_facet | Chen, Jiayu Jin, Jing Yao, Olivia X. M. |
| contents | Let $\overline{bt}(n)$ denote the number of overcubic partition triples of $n$. Nayaka, Dharmendra and Kumar proved some congruences modulo 8, 16 and 32 for $\overline{bt}(n)$. Recently, Saikia and Sarma established some congruences modulo 64 for $\overline{bt}(n)$ by using both elementary techniques and the theory of modular forms. In their paper, they also posed two conjectures on infinite families of congruences modulo 64 and 128 for $\overline{bt}(n)$. In this paper, we confirm the two conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proofs of two conjectures on congruences of overcubic partition triples Chen, Jiayu Jin, Jing Yao, Olivia X. M. Number Theory Let $\overline{bt}(n)$ denote the number of overcubic partition triples of $n$. Nayaka, Dharmendra and Kumar proved some congruences modulo 8, 16 and 32 for $\overline{bt}(n)$. Recently, Saikia and Sarma established some congruences modulo 64 for $\overline{bt}(n)$ by using both elementary techniques and the theory of modular forms. In their paper, they also posed two conjectures on infinite families of congruences modulo 64 and 128 for $\overline{bt}(n)$. In this paper, we confirm the two conjectures. |
| title | Proofs of two conjectures on congruences of overcubic partition triples |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.06941 |