Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Pubblicato
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.v56n2.108374Parole chiave:
k-generalized Fibonacci sequence, total multiplicity (en)sucesiones de Fibonacci k-generalizadas, multiplicidad total (es)
##submission.downloads##
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.
Riferimenti bibliografici
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.
Come citare
APA
ACM
ACS
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Scarica citazione
CrossRef Cited-by
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.
