On k-Fibonacci and k-Lucas numbers written as a product of two Pell numbers

被引：0

作者：

Rihane, Salah Eddine ^{[1
]}

机构：

[1] Natl Higher Sch Math, POB 75, Mahelma 16093, Algeria

来源：

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA | 2024年 / 30卷 / 01期

关键词：

k-Fibonacci numbers; k-Lucas numbers; Pell numbers; Linear form in logarithms; Reduction method;

D O I：

10.1007/s40590-024-00593-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let k >= 2. A generalization of the well-known Fibonacci and Lucas sequences are the k-Fibonacci and k-Lucas sequences. For these sequences, the first k terms are0,...,0,1 and 0,...,0,2,1, respectively, and each term afterwards is the sum of the preceding k terms. The principal objective of this manuscript is to identify all instances of k-Fibonacci and k-Lucas numbers that can be expressed as the product of two Pell numbers. This generalizes the result from Ref. Ddamulira et al.(Fibonacci Q 54: 11-18, 2016).

引用

页数：25

共 50 条

[1] On k-Fibonacci and k-Lucas numbers written as a product of two Pell numbers
Salah Eddine Rihane
Boletín de la Sociedad Matemática Mexicana, 2024, 30
[2] k-Fibonacci and k-Lucas Numbers as Product of Two Repdigits
Rihane, Salah Eddine
RESULTS IN MATHEMATICS, 2021, 76 (04)
[3] k-Fibonacci and k-Lucas Numbers as Product of Two Repdigits
Salah Eddine Rihane
Results in Mathematics, 2021, 76
[4] FERMAT k-FIBONACCI AND k-LUCAS NUMBERS
Bravo, Jhon J.
Herrera, Jose L.
MATHEMATICA BOHEMICA, 2020, 145 (01): : 19 - 32
[5] The Generalized k-Fibonacci and k-Lucas Numbers
Uslu, K.
Taskara, N.
Kose, H.
ARS COMBINATORIA, 2011, 99 : 25 - 32
[6] On Relationship Among a New Family of k-Fibonacci, k-Lucas Numbers, Fibonacci and Lucas Numbers
Ozkan, Engin
Altun, Ipek
Gocer, Ali Aykut
CHIANG MAI JOURNAL OF SCIENCE, 2017, 44 (04): : 1744 - 1750
[7] k-Fibonacci and k-Lucas numbers as (l, m)-antipalindromic numbers
Brahmi, Adel
Mokhtar, Ahmed Ait
Rihane, Salah Eddine
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2025, 31 (02):
[8] Symmetric functions of the k-Fibonacci and k-Lucas numbers
Boussayoud, Ali
Kerada, Mohamed
Araci, Serkan
Acikgoz, Mehmet
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2021, 14 (03)
[9] k-Fibonacci numbers and k-Lucas numbers and associated bipartite graphs
Lee, Gwangyeon
TURKISH JOURNAL OF MATHEMATICS, 2022, 46 (03) : 884 - 893
[10] Multiplicative dependence between k-Fibonacci and k-Lucas numbers
Carlos A. Gómez
Jhonny C. Gómez
Florian Luca
Periodica Mathematica Hungarica, 2020, 81 : 217 - 233

← 1 2 3 4 5 →