First, we examine the case $L_{(2n-1)m}/L_{m}$ and then we obtain $L_{\left( 2n-1\right) m}$ using different forms of Lucas numbers.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:The Lucas number sequence is a popular number sequence that has been described as similar to the Fibonacci number sequence.
📊
Key Findings & Data:Carlitz (1964) examined the requirement that a given Lucas number can be divided by another Lucas number.
💡
Conclusion & Impact:First, we examine the case $L_{(2n-1)m}/L_{m}$ and then we obtain $L_{\left( 2n-1\right) m}$ using different forms of Lucas numbers.
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 (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 $L_{(2n-1)m}/L_{m}$ and then we obtain $L_{\left( 2n-1\right) m}$ using different forms of Lucas numbers.
ŞAHİN, A., KARAGÖL, S. (2021). Some Divisibility Properties of Lucas Numbers. Turkish Journal of Mathematics and Computer Science, Cilt: 13 - Sayı: 2, 234–238. https://ajindex.com/articles/399334
Carlitz, L., A Note On Fibonacci numbers, Fibonacci Quarterly, 2(1)(1964), 15–28
Carlitz, L., Hunter, J.A.H., Sum of powers of Fibonacci and Lucas numbers, Fibonacci Quarterly, 7(5)(1969), 467–473
Carlitz, L., A Conjecture concerning Lucas numbers, Fibonacci Quarterly, 10(5)(1972), 526–550
Di Porto, A., Filipponi, P., A Probabilistic Primality Test Based on the Properties of Certain Generalized Lucas Numbers. In: Barstow D. et al. (eds) Advances in Cryptology, EUROCRYPT 88. EUROCRYPT 1988. Lecture Notes in Computer Science, vol 330. Springer, Berlin, Heidelberg, 1988
Hoggatt Jr., V.E., An application of the Lucas triangle, Fibonacci Quarterly, 8(4)(1970), 360–364