Common Values of Generalized Fibonacci and Leonardo Sequences

被引：0
|
作者：
Tripathy, Bibhu Prasad [1 ]
Patel, Bijan Kumar [1 ]
机构：
[1] KIIT Univ Bhubaneswar, Sch Appl Sci, Dept Math, Bhubaneswar 751024, Odisha, India
来源：
JOURNAL OF INTEGER SEQUENCES | 2023年 / 26卷 / 06期
关键词：
k-generalized Fibonacci number; Leonardo number; linear form in logarithms; reduction method; K-FIBONACCI;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For an integer k > 2, let F (k) n be the k-generalized Fibonacci sequence that starts with 0, ... , 0,1,1 (k terms) and each term afterwards is the sum of k preceding terms. In this paper, we find all the k-generalized Fibonacci numbers that are Leonardo numbers. More explicitly, we solve the Diophantine equation F (k) n = Lem in positive integers n, k, m with k > 2.
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页数：14
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