Solutions to a Pillai-type equation involving Tribonacci numbers and S-units
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909152074268672 |
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| author | Batte, Herbert Luca, Florian |
| author_facet | Batte, Herbert Luca, Florian |
| contents | Let $ \{T_n\}_{n\geq 0} $ be the sequence of Tribonacci numbers. In this paper, we study the exponential Diophantine equation $T_n-2^x3^y=c$, for $n,x,y\in \mathbb{Z}_{\ge0}$. In particular, we show that there is no integer $c$ with at least six representations of the form $T_n-2^x3^y$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17953 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions to a Pillai-type equation involving Tribonacci numbers and S-units Batte, Herbert Luca, Florian Number Theory 11B39, 11D61, 11D45, 11Y50 Let $ \{T_n\}_{n\geq 0} $ be the sequence of Tribonacci numbers. In this paper, we study the exponential Diophantine equation $T_n-2^x3^y=c$, for $n,x,y\in \mathbb{Z}_{\ge0}$. In particular, we show that there is no integer $c$ with at least six representations of the form $T_n-2^x3^y$. |
| title | Solutions to a Pillai-type equation involving Tribonacci numbers and S-units |
| topic | Number Theory 11B39, 11D61, 11D45, 11Y50 |
| url | https://arxiv.org/abs/2403.17953 |