Abstract

A generalization of the well-known Fibonacci sequence is the k-generalized Fibonacci sequence whose first k terms are 0, . . . , 0, 1 and each term afterwards is the sum of the preceding k terms. In this paper, by using a lower bound to linear forms in logarithms of algebraic numbers due to Matveev and some argument of the theory of continued fractions, we find all the members of F^(k) which are close to a power of 2. This paper continues and extends the previous work of Chern and Cui which investigated the Fibonacci numbers close to a power of 2.

中文翻译：

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k−斐波那契数接近 2 的幂

摘要

广为人知的斐波那契数列的一个推广是k推广的斐波那契数列，其前k项是 0 , . . . , 0 , 1 之后的每一项都是前面k项的总和。在本文中，通过使用由于 Matveev 和连分数理论的一些论据而在代数数的对数中线性形式的下界，我们找到了F ^(k)的所有成员，它们都接近 2 的幂。这论文继续并扩展了 Chern 和 Cui 之前研究接近 2 次方的斐波那契数的工作。