Powers of two in generalized fibonacci sequences
The $k-$generalized Fibonacci sequence $\big(F_{n}^{(k)}\big)_{n}$ resembles the Fibonacci sequence in that it starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we are interested in finding powers of two that appear in $k-$generaliz...
- Autores:
-
Bravo, Jhon J.
Luca, Florian
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2012
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/42254
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/42254
http://bdigital.unal.edu.co/32351/
- Palabra clave:
- Fibonacci numbers
Lower bounds for nonzero linear forms in logarithms of algebraic numbers
11B39
11J86
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | The $k-$generalized Fibonacci sequence $\big(F_{n}^{(k)}\big)_{n}$ resembles the Fibonacci sequence in that it starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we are interested in finding powers of two that appear in $k-$generalized Fibonacci sequences; i.e., we study the Diophantine equation $F_n^{(k)}=2^m$ in positive integers $n,k,m$ with $k\geq 2$. |
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