Powers of Two in Generalized Fibonacci Sequences

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.

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Bibliographic Details
Main Authors: BRAVO,JHON J., LUCA,FLORIAN
Format: Digital revista
Language:English
Published: Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas 2012
Online Access:http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262012000100005
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Summary: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.