k-Fibonacci and k-Lucas Numbers as Product of Two Repdigits

被引：2

作者：

Rihane, Salah Eddine ^{[1
]}

机构：

[1] Univ Ctr Mila, Dept Math & Comp Sci, BP 26, Mila 43000, Algeria

来源：

RESULTS IN MATHEMATICS | 2021年 / 76卷 / 04期

关键词：

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

D O I：

10.1007/s00025-021-01526-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let k >= 2. A generalization of the well-known Fibonacci and Lucas sequences are the k-Fibonacci and k-Lucas sequences, respectively. For these sequences the first k terms are 0, ... , 0,1 and 0, ... , 0, 2, 1, respectively, and each term afterwards is the sum of the preceding k terms. In this manuscript, our main objective is to find all k-Fibonacci and k-Lucas numbers which are product of two repdigits. This generalizes the result from Erduvan and Keskin (Turk J Math 43: 2142-2153, 2019).

引用

页数：20

共 50 条

[21] On the Binomial Sums of k-Fibonacci and k-Lucas sequences
Yilmaz, N.
Taskara, N.
Uslu, K.
Yazlik, Y.
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C, 2011, 1389
[22] A DIOPHANTINE EQUATION IN k-FIBONACCI NUMBERS AND REPDIGITS
Bravo, Jhon J.
Gomez, Carlos A.
Luca, Florian
COLLOQUIUM MATHEMATICUM, 2018, 152 (02) : 299 - 315
[23] The generalized k-Fibonacci polynomials and generalized k-Lucas polynomials
Tastan, Merve
Ozkan, Engin
Shannon, Anthony G.
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2021, 27 (02) : 148 - 158
[24] Triangular truncation of k-Fibonacci and k-Lucas circulant matrices
Dixon, John
Goldenberg, Michael
Mathes, Ben
Sukiennik, Justin
LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 440 : 177 - 187
[25] Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions
Ramirez, Jose L.
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2015, 23 (02): : 201 - 212
[26] Invertibility and Explicit Inverses of Circulant-Type Matrices with k-Fibonacci and k-Lucas Numbers
Jiang, Zhaolin
Gong, Yanpeng
Gao, Yun
ABSTRACT AND APPLIED ANALYSIS, 2014,
[27] On k-Fibonacci numbers expressible as product of two Balancing or Lucas-Balancing numbers
Rihane, Salah Eddine
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2025, 56 (01): : 339 - 356
[28] On k-Fibonacci numbers expressible as product of two Balancing or Lucas-Balancing numbers
Rihane, Salah Eddine
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023,
[29] Some k-Fibonacci and k-Lucas Identities by a Matrix Approach with Applications
Puangjumpa, Piyanut
THAI JOURNAL OF MATHEMATICS, 2022, 20 (01): : 417 - 423
[30] Some new properties of hyperbolic k-Fibonacci and k-Lucas octonions
Godase, A. D.
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2024, 30 (01) : 100 - 110

← 1 2 3 4 5 →