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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.v56n2.108374Mots-clés :
k-generalized Fibonacci sequence, total multiplicity (en)sucesiones de Fibonacci k-generalizadas, multiplicidad total (es)
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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.
Références
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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
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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.
