Original scientific paper

k-generalized Fibonacci numbers of the form 1+2^{n_1}+4^{n_2}+\cdots+(2^{k})^{n_k}

Carlos Alexis Gómez Ruiz orcid.org/0000-0003-1126-2973 ; Departamento de Matematicas, Universidad del Valle, Santiago de Cali, Colombia
Florian Luca ; School of Mathematics, University of the Witwatersrand, South Africa

Abstract

A generalization of the well-known Fibonacci sequence is the k-generalized Fibonacci sequence (F_n^{(k)})_{n>= 2-k} whose first k terms are 0, ..., 0, 1 and each term afterwards is the sum of the preceding k terms. In this paper, we investigate k-generalized Fibonacci numbers written in the form 1+2^{n_1}+4^{n_2}+\cdots+(2^{k})^{n_k}, for non-negative integers n_i, with n_k >= max{ n_i | 1<= i <= k-1}.

Keywords

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

Hrčak ID:

129579

URI

https://hrcak.srce.hr/129579

Publication date:

5.12.2014.

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