Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts

Attila Pethö; László Szalay

doi:10.15446/recolma.v56n2.108374

Veröffentlicht

2023-04-17

Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts

Cotas superiores de las soluciones de F(2k)n = +F(2k)m con subíndices negativos

DOI:

https://doi.org/10.15446/recolma.v56n2.108374

Schlagworte:

k-generalized Fibonacci sequence, total multiplicity (en)
sucesiones de Fibonacci k-generalizadas, multiplicidad total (es)

Downloads

PDF (English)

Autor/innen

Attila Pethö University of Debrecen
László Szalay University of Sopron

Abstract (en)
Abstract (es)

In this paper, we provide an explicit upper bound on the absolute value of the solutions n < m < 0 to the Diophantine equation F^(k)_n = ±F^(k)_m, assuming k is even. Here {F^(k)_n}_{n ∈ Z} denotes the k-generalized Fibonacci sequence. The upper bound depends only on k.

En este artículo presentamos una cota superior explícita para el valor absoluto de las soluciones con n < m < 0 de la ecuación Diofantina F^(k)_n = ±F^(k)_m, bajo la hipótesis que k es par. En la ecuación anterior {F^(k)_n}_{n ∈ Z} denota la sucesión de Fibonacci k-generalizada. La cota superior sólo depende de k.

Literaturhinweise

E. F. Bravo, C. A. Gómez, and F. Luca, Total multiplicity of the Tribonacci sequence, Colloq. Math. 159 (2020), 71-76. DOI: https://doi.org/10.4064/cm7730-2-2019

E. F. Bravo, C. A. Gómez, F. Luca, A. Togbé, and B. Kafle, On a conjecture about total multiplicity of Tribonacci sequence, Colloq. Math. 159 (2020), 61-69. DOI: https://doi.org/10.4064/cm7729-2-2019

G. P. B. Dresden and Z. Du, A simplified Binet formula for k-generalized Fibonacci numbers, J. Integer Seq. 17 (2014), Article 14.4.7, 9pp.

A. Dubickas, On the distance between two algebraic numbers, Bull. Malays. Math. Sci. Soc. 43 (2020), 3049-3064. DOI: https://doi.org/10.1007/s40840-019-00855-0

C. A. Gómez and F. Luca, On the zero-multiplicity of a fifth-order linear recurrence, Int. J. Number Theor. 15 (2019), 585-595. DOI: https://doi.org/10.1142/S1793042119500301

A. Pethö, On the k-generalized Fibonacci numbers with negative indices, Publ. Math. Debrecen 98 (2021), 401-418. DOI: https://doi.org/10.5486/PMD.2021.8912

D. A. Wolfram, Solving generalized Fibonacci recurrences, Fibonacci Quart. 36 (1988), 129-145.

Zitationsvorschlag

APA

Pethö, A. und Szalay, L. (2023). Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts. Revista Colombiana de Matemáticas, 56(2), 179–187. https://doi.org/10.15446/recolma.v56n2.108374

ACM

[1]

Pethö, A. und Szalay, L. 2023. Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts. Revista Colombiana de Matemáticas. 56, 2 (Apr. 2023), 179–187. DOI:https://doi.org/10.15446/recolma.v56n2.108374.

ACS

(1)

Pethö, A.; Szalay, L. Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts. rev.colomb.mat 2023, 56, 179-187.

ABNT

PETHÖ, A.; SZALAY, L. Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts. Revista Colombiana de Matemáticas, [S. l.], v. 56, n. 2, p. 179–187, 2023. DOI: 10.15446/recolma.v56n2.108374. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/108374. Acesso em: 22 jan. 2025.

Chicago

Pethö, Attila, und László Szalay. 2023. „Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts“. Revista Colombiana De Matemáticas 56 (2):179-87. https://doi.org/10.15446/recolma.v56n2.108374.

Harvard

Pethö, A. und Szalay, L. (2023) „Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts“, Revista Colombiana de Matemáticas, 56(2), S. 179–187. doi: 10.15446/recolma.v56n2.108374.

IEEE

[1]

A. Pethö und L. Szalay, „Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts“, rev.colomb.mat, Bd. 56, Nr. 2, S. 179–187, Apr. 2023.

MLA

Pethö, A., und L. Szalay. „Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts“. Revista Colombiana de Matemáticas, Bd. 56, Nr. 2, April 2023, S. 179-87, doi:10.15446/recolma.v56n2.108374.

Turabian

Pethö, Attila, und László Szalay. „Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts“. Revista Colombiana de Matemáticas 56, no. 2 (April 17, 2023): 179–187. Zugegriffen Januar 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/108374.

Vancouver

1.

Pethö A, Szalay L. Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts. rev.colomb.mat [Internet]. 17. April 2023 [zitiert 22. Januar 2025];56(2):179-87. Verfügbar unter: https://revistas.unal.edu.co/index.php/recolma/article/view/108374

Bibliografische Angaben herunterladen

CrossRef Cited-by

1

1. Eric Fernando Bravo. (2023). Common Values of Padovan and Perrin Sequences. Mediterranean Journal of Mathematics, 20(5) https://doi.org/10.1007/s00009-023-02467-2.