# Powers of two in generalized fibonacci sequences

Bravo, Jhon J. and Luca, Florian (2012) Powers of two in generalized fibonacci sequences. Revista Colombiana de Matemáticas; Vol. 46, núm. 1 (2012); 67-79 0034-7426 .

Texto completo

 Vista previa

420kB

4kB

## Resumen

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 $k\geq 2$.

Tipo de documento:Artículo - Article
Palabras clave:Fibonacci numbers, Lower bounds for nonzero linear forms in logarithms of algebraic numbers, 11B39, 11J86