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

Published

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

Keywords:

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

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Authors

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.

References

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.

How to Cite

APA

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

IEEE

[1]

A. Pethö and L. Szalay, “Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts”, rev.colomb.mat, vol. 56, no. 2, pp. 179–187, Apr. 2023.

MLA

Pethö, A., and L. Szalay. “Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts”. Revista Colombiana de Matemáticas, vol. 56, no. 2, Apr. 2023, pp. 179-87, doi:10.15446/recolma.v56n2.108374.

Turabian

Pethö, Attila, and 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. Accessed January 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]. 2023 Apr. 17 [cited 2025 Jan. 22];56(2):179-87. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/108374

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