Some Divisibility Properties of Lucas Numbers

Abstract

The Lucas number sequence is a popular numbersequence that has been described as similar to the Fibonacci numbersequence. 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 (1964) examined the requirement that agiven 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 LucasNumbers. First, we examine the case $L_{(2n-1)m}/L_{m}$ and then we obtain $L_{left( 2n-1right) m}$ using different forms of Lucas numbers.