Services on Demand
Journal
Article
Indicators
Cited by SciELO
Access statistics
Related links
Cited by Google
Similars in SciELO
Similars in Google
Share
Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Abstract
GOMEZ, CARLOS ALEXIS and LUCA, FLORIAN. Power of Two--Classes in k--Generalized Fibonacci Sequences. Rev.colomb.mat. [online]. 2014, vol.48, n.2, pp.219-234. ISSN 0034-7426. https://doi.org/10.15446/recolma.v48n2.54128.
The k-generalized Fibonacci sequence \big(Fn(k)\big)n\geq 2-k is the linear recurrent sequence of order k, whose first k terms are 0, …, 0, 1 and each term afterwards is the sum of the preceding k terms. Two or more terms of a k-generalized Fibonacci sequence are said to be in the same power of two-class if the largest odd factors of the terms are identical. In this paper, we show that for each k\ge 2, there are only two kinds of power of two-classes in a k-generalized Fibonacci sequence: one, whose terms are all the powers of two in the sequence and the other, with a single term.
Keywords : k--Generalized Fibonacci numbers; Lower bounds for nonzero linear forms in logarithms of algebraic numbers.