A Pillai-Catalan-type problem involving Fibonacci numbers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909313941897216 |
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| author | Ibrahimov, Seyran S. Mahmudov, Nazim I. |
| author_facet | Ibrahimov, Seyran S. Mahmudov, Nazim I. |
| contents | This paper addresses A Pillai-Catalan-type problem assosiated with Fibonacci numbers. Let $F_{n}$ be the Fibonacci numbers defined by the recurrence relation $F_{1}=1$, $F_{2}=1$ and $F_{n}=F_{n-1}+F_{n-2}$ for all $n\geq 3$. We will find all positive integer solution to the equation $3^{x}-F_{n}2^{y}=1$ using properties of Fibonacci numbers, linear forms of logarithms, and the Baker-Davenport reduction method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_08205 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Pillai-Catalan-type problem involving Fibonacci numbers Ibrahimov, Seyran S. Mahmudov, Nazim I. Number Theory This paper addresses A Pillai-Catalan-type problem assosiated with Fibonacci numbers. Let $F_{n}$ be the Fibonacci numbers defined by the recurrence relation $F_{1}=1$, $F_{2}=1$ and $F_{n}=F_{n-1}+F_{n-2}$ for all $n\geq 3$. We will find all positive integer solution to the equation $3^{x}-F_{n}2^{y}=1$ using properties of Fibonacci numbers, linear forms of logarithms, and the Baker-Davenport reduction method. |
| title | A Pillai-Catalan-type problem involving Fibonacci numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.08205 |