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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.56 no.2 Bogotá jul./dez. 2022 Epub 05-Jan-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
1. E. F. Bravo, C. A. Gómez, and F. Luca, Total multiplicity of the Tribonacci sequence, Colloq. Math. 159 (2020), 71-76. [ Links ]
2. 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. [ Links ]
3. 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. [ Links ]
4. A. Dubickas, On the distance between two algebraic numbers, Bull. Malays. Math. Sci. Soc. 43 (2020), 3049-3064. [ Links ]
5. C. A. Gómez and F. Luca , On the zero-multiplicity of a fifth-order linear recurrence, Int. J. Number Theor. 15 (2019), 585-595. [ Links ]
6. A. Pethő, On the k-generalized Fibonacci numbers with negative indices, Publ. Math. Debrecen 98 (2021), 401-418. [ Links ]
7. D. A. Wolfram, Solving generalized Fibonacci recurrences, Fibonacci Quart. 36 (1988), 129-145. [ Links ]
Received: June 05, 2020; Accepted: April 01, 2021