Genelleştirilmiş Fibonacci ve Lucas sayılarını içeren bazı özdeşlikler ve diofant denklemleri

In the first chapter, firstly, Fibonacci and Lucas numbers are mentioned briefly. Also the definitions of the generalized Fibonacci and Lucas sequences are given. Then, the review of the literature concerning generalized Fibonacci and Lucas sequences are given.In the second chapter, some identities and summation formulas containing generalized Fibonacci and Lucas numbers are obtained. Some of them are well known while the remaining ones new. Using some of these identities and summation formulas, it is given some congruences concerning generalized Fibonacci and Lucas numbers such as,and.Fibonacci and Lucas numbers of the form are determined after some fundamental theorems and identities concerning Fibonacci and Lucas numbers are given in the third chapter.In the fourth chapter, generalized Fibonacci and Lucas numbers of the form are determined under some assumptions using congruences concerning generalized Fibonacci and Lucas numbers given in the second chapter.Key Words: Fibonacci and Lucas Numbers, Generalized Fibonacci and Lucas Numbers, Congruences, Diophantine Equations.