Coincidences in generalized Fibonacci sequences

被引：37

作者：

Bravo, Jhon J. ^{[1
]}

Luca, Florian ^{[2
]}

机构：

[1] Univ Cauca, Dept Matemat, Popayan, Colombia

[2] Inst Ciencias Nucl UNAM, Fdn Marcos Moshinsky, CU, Apdo Postal 70-543, Mexico City 04510, DF, Mexico

来源：

JOURNAL OF NUMBER THEORY | 2013年 / 133卷 / 06期

关键词：

Fibonacci numbers; Lower bounds for non-zero linear forms in logarithms of algebraic numbers;

D O I：

10.1016/j.jnt.2012.11.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The k-generalized Fibonacci sequence (F-n((k)))(n) resembles the Fibonacci sequence in that it starts with 0, ... ,0, 1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we are interested in finding the integers that appear in different generalized Fibonacci sequences; i.e., we study the Diophantine equation F-n((k)) = F-m((l)) in positive integers n, k, m, l with k, l >= 2. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：2121 / 2137

页数：17

共 6 条

[1] On a conjecture about repdigits in k-generalized Fibonacci sequences [J].