Resumo

GOMEZ, CARLOS ALEXIS  e  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(F_n^(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.

Palavras-chave : k--Generalized Fibonacci numbers; Lower bounds for nonzero linear forms in logarithms of algebraic numbers.

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