ON THE DIOPHANTINE EQUATION <i>F_n</i> + <i>F_m</i>=2<i><SUP>a</SUP></i>

作     者：Bravo, Jhon J. Luca, Florian 

作者机构：Univ Cauca Dept Matemat Calle 5 4-70 Popayan Cauca Colombia Univ Witwatersrand Sch Math POB Wits 2050 ZA-2050 Johannesburg South Africa 

出 版 物：《QUAESTIONES MATHEMATICAE》 (数学问题)

年 卷 期：2016年第39卷第3期

页      面：391-400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：Universidad del Cauca Colciencias from Colombia 

主　　题：Fibonacci numbers Zeckendorf representation linear forms in logarithms reduction method 

摘      要：In this paper, we find all the solutions of the title Diophantine equation in positive integer variables (n, m, (a), where F-k, is the kth term of the Fibonacci sequence. The proof of our main theorem uses lower bounds for linear forms in logarithms (Baker s theory) and a version of the Baker-Davenport reduction method in diophantine approximation.