A DIOPHANTINE EQUATION IN k-FIBONACCI NUMBERS AND REPDIGITS

被引：12

作者：

Bravo, Jhon J. ^{[1
]}

Gomez, Carlos A. ^{[2
]}

Luca, Florian ^{[3
,4
,5
]}

机构：

[1] Univ Cauca, Dept Matemat, Calle 5 4-70, Popayan, Colombia

[2] Univ Valle, Dept Matemat, Calle 13 100-00, Cali, Colombia

[3] Univ Witwatersrand, Sch Math, POB Wits, ZA-2050 Johannesburg, South Africa

[4] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

[5] Univ Ostrava, Fac Sci, Dept Math, 30 Dubna 22, Ostrava 70103 1, Czech Republic

来源：

COLLOQUIUM MATHEMATICUM | 2018年 / 152卷 / 02期

关键词：

generalized Fibonacci numbers; lower bounds for nonzero linear forms in logarithms of algebraic numbers; repdigits;

D O I：

10.4064/cm7149-6-2017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The k-generalized Fibonacci sequence {F-n((k))}(n) starts with the k values 0,... , 0,1 and each term afterwards is the sum of the k preceding terms. We study which members of this sequence are sums of two repdigts, extending a result of Diaz and Luca (2011) regarding Fibonacci numbers with this property.

引用

页码：299 / 315

页数：17

共 50 条

[31] Catalan Identity for the k-Fibonacci Numbers Proposal
Plaza, Angel
Falcon, Sergio
FIBONACCI QUARTERLY, 2019, 57 (02): : 177 - 177
[32] Dual-complex k-Fibonacci numbers
Aydin, Fugen Torunbalci
CHAOS SOLITONS & FRACTALS, 2018, 115 : 1 - 6
[33] On a Diophantine equation involving powers of Fibonacci numbers
Gueth, Krisztian
Luca, Florian
Szalay, Laszlo
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2020, 96 (04) : 33 - 37
[34] POWERS OF TWO AS SUMS OF TWO k-FIBONACCI NUMBERS
Bravo, Jhon J.
Gomez, Carlos A.
Luca, Florian
MISKOLC MATHEMATICAL NOTES, 2016, 17 (01) : 85 - 100
[35] Some Infinite Sums Related to the k-Fibonacci Numbers
Karaoglu, Onur
Uslu, Kemal
COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, 2018, 9 (04): : 651 - 659
[36] 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
[37] 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):
[38] Pillai's problem with k-Fibonacci and Pell numbers
Bravo, Jhon J.
Diaz, Maribel
Gomez, Carlos A.
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2021, 27 (10) : 1434 - 1455
[39] 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)
[40] Coincidence Between k-Fibonacci Numbers and Products of Two Fermat Numbers
Gueye, Alioune
Rihane, Salah Eddine
Togbe, Alain
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2022, 53 (02): : 541 - 552

← 1 2 3 4 5 →