Repdigits as sums of two <i>k</i>-Fibonacci numbers

作     者：Bravo, Jhon J. Luca, Florian 

作者机构：Univ Cauca Dept Matemat Popayan Cauca Colombia UNAM Juriquilla Math Inst Santiago De Queretaro 76230 Queretaro De Ar Mexico Univ Witwatersrand Sch Math Johannesburg South Africa 

出 版 物：《MONATSHEFTE FUR MATHEMATIK》 (数学月刊)

年 卷 期：2015年第176卷第1期

页      面：31-51页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：CONACyT from Mexico University of Cauca, Colciencias from Colombia Marcos Moshinsky Fellowship PAPIIT IN104512 CONACyT 163787 CONACyT 193539 

主　　题：Generalized Fibonacci numbers Repdigits Linear forms in logarithms Reduction method 

摘      要：For an integer , let be the -Fibonacci sequence which starts with ( terms) and each term afterwards is the sum of the preceding terms. In this paper, we find all repdigits (i.e., numbers with only one distinct digit in its decimal expansion) which are sums of two -Fibonacci numbers. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction method. This paper is an extended work related to our previous work (Bravo and Luca Publ Math Debr 82:623-639, 2013).