Fibonacci numbers which are concatenations of two repdigits

被引：36

作者：

Alahmadi, Adel ^{[1
]}

Altassan, Alaa ^{[1
]}

Luca, Florian ^{[1
,2
,3
]}

Shoaib, Hatoon ^{[1
]}

机构：

[1] King Abdulaziz Univ, Res Grp Algebra Struct & Its Applicat, Jeddah, Saudi Arabia

[2] Univ Witwatersrand, Sch Math, Johannesburg, South Africa

[3] Max Planck Inst Math, Bonn, Germany

来源：

QUAESTIONES MATHEMATICAE | 2021年 / 44卷 / 02期

关键词：

Fibonacci numbers; repdigit; linear forms in complex logarithms;

D O I：

10.2989/16073606.2019.1686439

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the only Fibonacci numbers that are concatenations of two repdigits are 13, 21, 34, 55, 89, 144, 233, 377.

引用

页码：281 / 290

页数：10

共 14 条

[1]

[Anonymous], 2011, P 14 INT C FIBONACCI

[2]

Banks WD, 2005, INT MATH RES NOTICES, V2005, P1

[3] On a conjecture about repdigits in k-generalized Fibonacci sequences [J].

Bravo, Jhon J. ;

Luca, Florian .

PUBLICATIONES MATHEMATICAE-DEBRECEN, 2013, 82 (3-4) :623-639

[4] On integers with identical digits [J].

Bugeaud, Y ;

Mignotte, M .

MATHEMATIKA, 1999, 46 (92) :411-417

[5] Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers [J].

Bugeaud, Yann ;

Mignotte, Maurice ;

Siksek, Samir .

ANNALS OF MATHEMATICS, 2006, 163 (03) :969-1018

[6] A generalization of a theorem of Baker and Davenport [J].

Dujella, A ;

Petho, A .

QUARTERLY JOURNAL OF MATHEMATICS, 1998, 49 (195) :291-306

[7]

Luca F., 2000, Quaest. Math, V23, P389, DOI [10.2989/16073600009485986, DOI 10.2989/16073600009485986]

[8]

Luca F., 2000, Portugaliae Math, V57, P243

[9]

Luca F, 2012, MATH COMMUN, V17, P1

[10]

Marques D., 2012, Rend. Istit. Mat. Univ. Trieste, V44, P393

← 1 2 →