Products of Tribonacci Numbers that are the Products of Factorials
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912634583908352 |
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| author | Das, Pranabesh Saunders, J. C. |
| author_facet | Das, Pranabesh Saunders, J. C. |
| contents | In 2014 Marques and Lengyel gave all of the solutions to the equation $T_n=m!$, where $T_n$ is the $n$th term of the Tribonacci sequence $0,1,1,2,4,7,13,24,\ldots$. In 2023 Alahmadi and Luca generalized their result to the equation $T_n=m_1!m_2!\cdots m_k!$ for every $k\in\mathbb{N}$, where $m_1\leq m_2\leq\ldots\leq m_k$ listing all the solutions to this equation. Here we generalize these results further and give all the solutions to $T_nT_{n+1}T_{n+2}\cdots T_{n+r}=m_1!m_2!\cdots m_k!$ and $ |T_{-n}T_{-n-1}T_{-n-2}\cdots T_{-n-r}|=m_1!m_2!\cdots m_k!$ for every $n,r\in\mathbb{N}$, where $m_1\leq m_2\leq\ldots\leq m_k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06520 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Products of Tribonacci Numbers that are the Products of Factorials Das, Pranabesh Saunders, J. C. Number Theory In 2014 Marques and Lengyel gave all of the solutions to the equation $T_n=m!$, where $T_n$ is the $n$th term of the Tribonacci sequence $0,1,1,2,4,7,13,24,\ldots$. In 2023 Alahmadi and Luca generalized their result to the equation $T_n=m_1!m_2!\cdots m_k!$ for every $k\in\mathbb{N}$, where $m_1\leq m_2\leq\ldots\leq m_k$ listing all the solutions to this equation. Here we generalize these results further and give all the solutions to $T_nT_{n+1}T_{n+2}\cdots T_{n+r}=m_1!m_2!\cdots m_k!$ and $ |T_{-n}T_{-n-1}T_{-n-2}\cdots T_{-n-r}|=m_1!m_2!\cdots m_k!$ for every $n,r\in\mathbb{N}$, where $m_1\leq m_2\leq\ldots\leq m_k$. |
| title | Products of Tribonacci Numbers that are the Products of Factorials |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.06520 |