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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.56 no.2 Bogotá July/Dec. 2022 Epub Jan 05, 2024
https://doi.org/10.15446/recolma.v56n2.108374
Original articles
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
1 University of Debrecen, Debrecen, Hungary
2 J. Selye University, Komárno, Slovakia
3 University of Sopron, Sopron, Hungary
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.
Keywords: k-generalized Fibonacci sequence; total multiplicity
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.
Palabras clave: sucesiones de Fibonacci k-generalizadas; multiplicidad total
References
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Received: June 05, 2020; Accepted: April 01, 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
