Some divisibility properties of Lucas numbers

In this thesis, the basic divisibility properties of integers were first explained. Definition of the Fibonacci number sequence was given. The Golden Ratio was mentioned briefly. The relationship between Lucas and Fibonacci numbers and the Golden Ratio was also touched on. The life of François Edouard Anatole Lucas was given in the study. An extensive literature review was conducted and the theorems of Fibonacci and Lucas number sequences was given. Divisibility properties in the Lucas numbers which had been found before and had formed the main point of our study were explained. Specifically, Carlitz (1964) acted on the condition that a Lucas number given by it can be divided into another Lucas number. Based on this condition, new features were found among Lucas numbers. The theorems found in study were proved and exemplified. The divisibility condition explored by Koşar (2013) for the Fibonacci number was examined. The new divisibility features found as a result of the researches were also used. It has been identified that any Lucas number, which was the main purpose of the study, could be divided into the what forces of another Lucas number.