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k-Pell numbers written as a product of two Narayana numbers
Números de Pell de tipo k que se representan como producto de dos números de Narayana
DOI:
https://doi.org/10.15446/recolma.v59n1.122859Palabras clave:
k-Pell numbers, Narayana’s cows sequence, linear forms in logarithms, reduction method (en)Números de Pell, sucesión de Narayana, formas lineares en logaritmos, método de reducción (es)
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For an integer k ≥ 2, let {P(k)n}n be the k-generalized Pell sequence which starts with 0, . . . , 0, 1(k terms) and each term afterwards is the sum of k preceding terms. The purpose of this paper is to determine all k-Pell numbers, which are the product of two of Narayana’s numbers. More precisely, we study the Diophantine equation
P(k)n = Nm Nl
in positive integers (n, k, m, l) with k ≥ 2, where {Nm}m is the Narayana’s cows sequence.
Para cada entero k ≥ 2, sea {P(k)n}n la k-sucesión de Pell que comienza en 0, . . . , 0, 1(los primeros k términos) y los términos siguientes se calculan como la suma de los k términos anteriores. El objetivo de este artículo es determinar cuáles números de la k-sucesión de Pell se pueden escribir como el producto de dos números de Narayana. De forma más precisa, estudiamos la ecuación Diofantina
P(k)n = Nm Nl
para enteros (n, k, m, l) con k ≥ 2, donde {Nm}m es la sucesión de Narayana.
Referencias
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