MERSENNE k-FIBONACCI NUMBERS

被引：0

作者：

Bravo, Jhon J. ^{[1
]}

Gomez, Carlos A. ^{[2
]}

机构：

[1] Univ Cauca, Dept Matemat, Calle 5 4-70, Popayan, Colombia

[2] Univ Valle, Dept Matemat, Calle 13 100-00, Cali, Colombia

来源：

GLASNIK MATEMATICKI | 2016年 / 51卷 / 02期

关键词：

Generalized Fibonacci numbers; Mersenne numbers; linear forms in logarithms; reduction method; CONJECTURE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For an integer k >= 2, let (F-n((k)))(n) be the k-Fibonacci sequence which starts with 0,..., 0, 1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we find all k-Fibonacci numbers which are Mersenne numbers, i.e., k-Fibonacci numbers that are equal to 1 less than a power of 2. As a consequence, for each fixed k, we prove that there is at most one Mersenne prime in (F-n((k)))n.

引用

页码：307 / 319

页数：13

共 17 条

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[9]

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[10]

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