Solutions of some exponential diophantineequations including the Fibonacci and Lucas numbers

This thesis consists of five chapters. In the first chapter, a brief history of Diophantine equations and the origin of Fibonacci and Lucas numbers are given. Then some Diophantine equations including Fibonacci and Lucas numbers are mentioned. In the second chapter, some definitions and theorems related to some integer sequences, continued fractions, field extension and logarithmic height of the algebraic numbers are given. In the third chapter, after the definition of linear forms in logarithms, Baker's theory and some important results of this theory are mentioned. Then Baker-Davenport's lemma and some useful versions of this lemma are given. In the fourth chapter, after giving previous studies and auxiliary theorems, some exponential Diophantine equations are solved with the help of lineer forms in logarithms. Firstly, the Fibonacci and Lucas numbers which can be written as the products of two natural numbers which all digits are the same on a certain base are determined. Then, the Lucas numbers which can be written in the form of concatenation of two natural numbers that all digits are the same are found. The fifth chapter consist of results and suggestions.