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(F_n^(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 F_n^(k)=2^m in positive integers n,k,m with k≥ 2.

Keywords : Fibonacci numbers; Lower bounds for nonzero linear forms in logarithms of algebraic numbers.

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