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

[1] On a Variant of an Identity Relating Cubes of Three Consecutive Fibonacci Numbers
Carlos A. Gómez
Jhonny C. Gómez
Florian Luca
Bulletin of the Malaysian Mathematical Sciences Society, 2023, 46
[2] Fibonacci numbers which are products of three Pell numbers and Pell numbers which are products of three Fibonacci numbers
Salah Eddine Rihane
Youssouf Akrour
Abdelaziz El Habibi
Boletín de la Sociedad Matemática Mexicana, 2020, 26 : 895 - 910
[3] Fibonacci numbers which are products of three Pell numbers and Pell numbers which are products of three Fibonacci numbers
Rihane, Salah Eddine
Akrour, Youssouf
El Habibi, Abdelaziz
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2020, 26 (03): : 895 - 910
[4] An Exponential Diophantine Equation Related to Powers of Three Consecutive Fibonacci Numbers
Patel, Bijan Kumar
Teh, Wen Chean
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2021, 44 (02) : 927 - 939
[5] An Exponential Diophantine Equation Related to Powers of Three Consecutive Fibonacci Numbers
Bijan Kumar Patel
Wen Chean Teh
Bulletin of the Malaysian Mathematical Sciences Society, 2021, 44 : 927 - 939
[6] FIBONACCI NUMBERS MODULO CUBES OF PRIMES
Sun, Zhi-Wei
TAIWANESE JOURNAL OF MATHEMATICS, 2013, 17 (05): : 1523 - 1543
[7] A Diophantine Equation With Powers of Three Consecutive k - Fibonacci Numbers
Gomez, Carlos A.
Gomez, Jhonny C.
Luca, Florian
RESULTS IN MATHEMATICS, 2024, 79 (04)
[8] On the distance between products of consecutive Fibonacci numbers and powers of Fibonacci numbers
Bravo, Jhon J.
Komatsu, Takao
Luca, Florian
INDAGATIONES MATHEMATICAE-NEW SERIES, 2013, 24 (01): : 181 - 198
[9] On Fibonacci numbers as sum of powers of two consecutive Tribonacci numbers
Alessandra Kreutz
Diego Marques
Pavel Trojovský
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022, 116
[10] On the sum of powers of two consecutive Fibonacci numbers
Marques, Diego
Togbe, Alain
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2010, 86 (10) : 174 - 176

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