SavedAdd your journal

Journals / Turkish Journal of Science / 2021 / Cilt: 6 Sayı: 3

The Period and Rank of the Complex-type Padovan-p Numbers Modulo m

Ömür Deveci(KAFKAS UNIVERSITY)0000-0001-5870-5298
Özgür Erdağ(KAFKAS UNIVERSITY)0000-0001-8071-6794
Pages
156–161
Publication Date
2021-12-30
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we give the relationships between the periods of the complex-type Padovan-p sequences modulo m and the orders of the cyclic groups produced.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the complex-type Padovan-p sequence modulo m and then we give some results concerning the periods and the ranks of these sequences for any p and m.
📊
Key Findings & Data:Furthermore, we produce the cyclic groups using the multiplicative orders of the generating matrices of the complex-type Padovan-p sequences when read modulo m.
💡
Conclusion & Impact:Finally, we give the relationships between the periods of the complex-type Padovan-p sequences modulo m and the orders of the cyclic groups produced.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:The complex-type Padovan-p sequence · Modulo · Period

Abstract

In this paper, we study the complex-type Padovan-p sequence modulo m and then we give some results concerning the periods and the ranks of these sequences for any p and m. Furthermore, we produce the cyclic groups using the multiplicative orders of the generating matrices of the complex-type Padovan-p sequences when read modulo m. Finally, we give the relationships between the periods of the complex-type Padovan-p sequences modulo m and the orders of the cyclic groups produced.

🔖

Cite This Article

Deveci, Ö., Erdağ, Ö. (2021). The Period and Rank of the Complex-type Padovan-p Numbers Modulo m. Turkish Journal of Science, Cilt: 6 Sayı: 3, 156–161. https://ajindex.com/articles/1557528

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Akuzum Y, Deveci O. The Hadamard-type k-step Fibonacci sequences in groups. Communications in Algebra. 48(7), 2020, 2844−2856.
  2. Aydin H, Dikici R. General Fibonacci sequences in finite groups. Fibonacci Quarterly. 36(3), 1998, 216−221.
  3. Campbell CM, Doostie H, Robertson EF. Fibonacci length of generating pairs in groups. In: Bergum, G. E., ed. Applications of Fibonacci Numbers. Vol. 3. Springer, Dordrecht: Kluwer Academic Publishers, 1990, pp. 27−35.
  4. Deveci O, Karaduman E. On the Padovan p-numbers. Hacettepe Journal of Mathematics and Statistics. 46(4), 2017, 579−592.
  5. Deveci O, Akuzum Y, Karaduman E. The Pell-Padovan p-Sequences and Its Applications. Utilitas Mathematica. 98, 2015, 327−347.
  6. Deveci O, Akuzum Y. The Cyclic Groups and The Semigroups via MacWilliams and Chebyshev Matrices. Journal of Mathematics Research. 6(2), 2014, 55−58.
  7. Deveci O, Shannon AG. The complex-type k-Fibonacci sequences and their applications. Communications in Algebra. 49(3), 2021, 1352−1367.
  8. Doostie H, Hashemi M. Fibonacci lengths involving the Wall number K(n). Journal of Applied Mathematics and Computing. 20(1-2), 2006, 171−180.
  9. Erdag O, Halıcı S, Deveci O. The Complex-Type Padovan-p Sequences. is submitted.
  10. Falcon S, Plaza A. k-Fibonacci sequences modulo m. Chaos, Solitons and Fractals. 41(1), 2009, 497−504.
  11. Karaduman E, Aydın H. k-nacci sequences in some special groups of finite order. Mathematical and Computer Modelling. 50(1-2), 2009, 53−58.
  12. Knox SW. Fibonacci sequences in finite groups, Fibonacci Quarterly. 30(2), 1992, 116−120.
  13. Lu K, Wang J. k-step Fibonacci sequence modulo m. Utilitas Mathematica. 71, 2006, 169−177.
  14. Ozkan E, Aydin H, Dikici R. 3-step Fibonacci series modulo m. Applied Mathematics and Computation. 143(1), 2003, 165−172.
  15. Wall DD. Fibonacci series modulo m, American Mathematical Monthly. 67(6), 1960, 525−532.
  16. Wilcox HJ. Fibonacci sequences of period n in Groups. Fibonacci Quarterly. 24(4), 1986, 356−361.