POWERS OF TWO AS SUMS OF TWO k-FIBONACCI NUMBERS

被引：96

作者：

Bravo, Jhon J. ^{[1
]}

Gomez, Carlos A. ^{[2
]}

Luca, Florian ^{[3
]}

机构：

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

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

[3] Univ Witwatersrand, Sch Math, Private Bag X3, ZA-2050 Johannesburg, South Africa

来源：

MISKOLC MATHEMATICAL NOTES | 2016年 / 17卷 / 01期

关键词：

generalized Fibonacci numbers; linear forms in logarithms; reduction method; GENERALIZED FIBONACCI; REPDIGITS;

D O I：

10.18514/MMN.2016.1505

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 search for powers of 2 which are sums of two k-Fibonacci numbers. The main tools used in this work are lower bounds for linear forms in logarithms and a version of the Baker-Davenport reduction method in diophantine approximation. This paper continues and extends the previous work of [4] and [2].

引用

页码：85 / 100

页数：16

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