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Dergiler / Turkish Journal of Mathematics and Computer Science / 2021 / Volume: 13 Issue: 2

Some Divisibility Properties of Lucas Numbers

Adem Şahin(TOKAT GAZİOSMANPAŞA ÜNİVERSİTESİ)0000-0001-5739-4117
Sadettin Karagöl(M. Emin Saraç AİHL, Tokat)0000-0002-3907-8927
Sayfa
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Yayın Tarihi
2021-12-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

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Amaç & Hipotez:The Lucas number sequence is a popular number sequence that has been described as similar to the Fibonacci number sequence.
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Temel Bulgular & Veri:Carlitz (1964) examined the requirement that a given Lucas number can be divided by another Lucas number.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Lucas sequence · divisibility · Recurrence relation

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 (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.

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Bu Makaleye Atıf Yap

Şahin, A., Karagöl, S. (2021). Some Divisibility Properties of Lucas Numbers. Turkish Journal of Mathematics and Computer Science, Volume: 13 Issue: 2. https://doi.org/10.47000/tjmcs.783597

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Kaynakça (11)

  1. Carlitz, L., A Note On Fibonacci numbers, Fibonacci Quarterly, 2(1)(1964), 15–28.
  2. Carlitz, L., Hunter, J.A.H., Sum of powers of Fibonacci and Lucas numbers, Fibonacci Quarterly, 7(5)(1969), 467–473.
  3. Carlitz, L., A Conjecture concerning Lucas numbers, Fibonacci Quarterly, 10(5)(1972), 526–550.
  4. 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.
  5. Hoggatt Jr., V.E., An application of the Lucas triangle, Fibonacci Quarterly, 8(4)(1970), 360–364.
  6. Hoggatt Jr., V.E., Bergum, G.E., Divisibility and congruence relations, Fibonacci Quarterly, 12(2)(1974), 189–195.
  7. Keskin, R., Demirturk Bitim, B., Fibonacci and Lucas congruences and their applications, Acta Math. Sinica, 27(4)(2011),725–736.
  8. Koshy, T., New Fibonacci and Lucas identities, The Mathematical Gazette, 82(495)(1998), 481–484.
  9. Koshy, T., The convergence of a Lucas series, The Mathematical Gazette, 83(497)(1999), 272–274.
  10. Koshy, T., Fibonacci and Lucas Numbers With Aplications. John Wiley & Sons Inc., New York, USA, 2001.
  11. Vajda, S., Fibonacci and Lucas Numbers and The Golden Section, Ellis Horwood Limited, Chichester, England, 1989.