Markov triples with k-generalized Fibonacci components

被引：4

作者：

Gomez, Carlos A. ^{[1
]}

Gomez, Jhonny C. ^{[1
]}

Luca, Florian ^{[2
,3
,4
]}

机构：

[1] Univ Valle, Dept Matemat, Cali, Colombia

[2] Univ Witwatersrand, Sch Math, Johannesburg, South Africa

[3] King Abdulaziz Univ, Res Grp Algebra Struct & Applicat, Jeddah, Saudi Arabia

[4] UNAM, Ctr Ciencias Matemat, Morelia, Michoacan, Mexico

来源：

ANNALES MATHEMATICAE ET INFORMATICAE | 2020年 / 52卷

关键词：

Markov equation; Markov triples; k-generalized Fibonacci numbers; k-Fibonacci numbers;

D O I：

10.33039/ami.2020.06.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find all triples (x, y, z) of k-Fibonacci numbers which satisfy the Markov equation x(2) + y(2) + z(2) = 3xyz. This paper continues and extends previous work by Luca and Srinivasan [6].

引用

页码：107 / 115

页数：9

共 8 条

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Bravo, Jhon J. ;

Gomez, Carlos A. ;

Luca, Florian .

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[2]

BRAVO JHON J., 2012, Rev.colomb.mat., V46, P67

[3]

Dresden GPB, 2014, J INTEGER SEQ, V17

[4] AN EXPONENTIAL DIOPHANTINE EQUATION RELATED TO THE SUM OF POWERS OF TWO CONSECUTIVE k-GENERALIZED FIBONACCI NUMBERS [J].

Gomez Ruiz, Carlos Alexis ;

Luca, Florian .

COLLOQUIUM MATHEMATICUM, 2014, 137 (02) :171-188

[5]

Hua LK, 1981, APPL NUMBER THEORY N

[6]

Luca F, 2018, FIBONACCI QUART, V56, P126

[7]

Sloane N.J.A., The on-line encyclopedia of integer sequences (A007323), DOI DOI 10.1371/journal.pone.0096223

[8]

Wolfram DA, 1998, FIBONACCI QUART, V36, P129

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