On a Variant of an Identity Relating Cubes of Three Consecutive Fibonacci Numbers

被引：0

作者：

Gomez, Carlos A. ^{[1
,2
]}

Gomez, Jhonny C. ^{[3
]}

Luca, Florian ^{[4
,5
,6
]}

机构：

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

[2] Univ Valle Algebra Teoria Numeros & Aplicac, Res Grp ALTENUA, Colciencias Code COL0017217, Cali, Colombia

[3] Univ Libre Secc Pereira, Fac Ciencias Econ Adm & Contables, Ave Amer Carrera 28 96-102, Pereira, Colombia

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

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

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

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2023年 / 46卷 / 02期

关键词：

Fibonacci numbers; Diophantine exponential equation; Linear form in logarithms; Reduction method;

D O I：

10.1007/s40840-022-01439-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

F-n+1(3) + F-n(3) - F-n-1(3) = F-3n, for all n >= 1, is a well-known identity fulfilled by the Fibonacci numbers. In this paper, we study a variant of this identity, replacing the cubic powers by a general power on the left-hand side and allowing an additional unknown exponent on the right-hand side.

引用

页数：31

共 29 条

[21] On the representation of Fibonacci and Lucas numbers as the sum of three squares
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[22] ON FACTORIALS EXPRESSIBLE AS SUMS OF AT MOST THREE FIBONACCI NUMBERS
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[23] On the representation of Fibonacci and Lucas numbers as the sum of three squares
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[26] On a variant of Pillai’s problem involving S-units and Fibonacci numbers
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[27] On a variant of Pillai's problem involving S-units and Fibonacci numbers
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[28] ON A SYSTEM OF THREE DIFFERENCE EQUATIONS OF HIGHER ORDER SOLVED IN TERMS OF LUCAS AND FIBONACCI NUMBERS
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MATHEMATICA SLOVACA, 2020, 70 (03) : 641 - 656
[29] A Diophantine Equation With Powers of Three Consecutive k-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k-$$\end{document}Fibonacci Numbers
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Results in Mathematics, 2024, 79 (4)

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