Some Divisibility Properties of Lucas Numbers

Authors : Adem ŞAHİN, Sadettin KARAGÖL

Pages : 234-238

Doi:10.47000/tjmcs.783597

View : 13 | Download : 9

Publication Date : 2021-12-31

Article Type : Research Paper

Abstract :The Lucas number sequence is a popular number sequence that has been described as similar to the Fibonacci number sequence. A lot of research has been done on this number sequence. Some of these studies are on the divisibility properties of this number sequence. Carlitz insert ignore into journalissuearticles values(1964); examined the requirement that a given Lucas number can be divided by another Lucas number. After that, many studies have been done on this subject. In the present article, we obtain some divisibility properties of the Lucas Numbers. First, we examine the case $L_{insert ignore into journalissuearticles values(2n-1);m}/L_{m}$ and then we obtain $L_{\leftinsert ignore into journalissuearticles values( 2n-1\right); m}$ using different forms of Lucas numbers.
Keywords : Lucas sequence, divisibility, Recurrence relation