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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Abstract
BRAVO, JHON J. and LUCA, FLORIAN. Powers of Two in Generalized Fibonacci Sequences. Rev.colomb.mat. [online]. 2012, vol.46, n.1, pp.67-79. ISSN 0034-7426.
The k-generalized Fibonacci sequence \big(Fn(k)\big)n resembles the Fibonacci sequence in that it starts with 0,…,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 Fn(k)=2m in positive integers n,k,m with k≥ 2.
Keywords : Fibonacci numbers; Lower bounds for nonzero linear forms in logarithms of algebraic numbers.