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Dergiler / Celal Bayar Üniversitesi Fen Bilimleri Dergisi / 2017 / Cilt: 13 - Sayı: 1

On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix

Yasemin TAŞYURDU
Zülküf DİLMEN
Sayfa
165–169
Yayın Tarihi
2022-10-12
DOI
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Also, the period of this sequence is compared with Wall number of Fibonacci sequence and it was shown that this period always was an even number

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, { } Fibonacci sequence was defined over an arbitrary ring and its some properties are investigated.The terms of this sequence are derivated by Tridiagonal determinant of the matrix.
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Temel Bulgular & Veri:It was seen that order of cyclic group generated with matrix = [] is equal to the period of this sequence where , are arbitrary elements of the ring.
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Sonuç & Katkı:Also, the period of this sequence is compared with Wall number of Fibonacci sequence and it was shown that this period always was an even number
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this study, { } Fibonacci sequence was defined over an arbitrary ring and its some properties are investigated.The terms of this sequence are derivated by Tridiagonal determinant of the matrix. It was shown that this sequence is periodic and their period is obtained. It was shown that the sequence obtained by reducing modulo coefficient and exponent of each Fibonacci sequence in arbitrary rings is periodic. It was seen that order of cyclic group generated with matrix = [] is equal to the period of this sequence where , are arbitrary elements of the ring. Also, the period of this sequence is compared with Wall number of Fibonacci sequence and it was shown that this period always was an even number

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Bu Makaleye Atıf Yap

TAŞYURDU, Y., DİLMEN, Z. (2022). On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 13 - Sayı: 1, 165–169. https://ajindex.com/articles/472342

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Kaynakça (12)

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  10. Taşyurdu, Y.; Gültekin, İ. On period of Fibonacci sequences in finite rings with identity of order 𝑝 2. Journal of Mathematics and System Science. 2013; 3, 349- 352
  11. Taşyurdu, Y.; Gültekin, İ. The Period of Fibonacci Sequences Over The Finite Field of Order 𝑝 2. New Trends in Mathematical Sciences. 2016; 4, 248-255 [12] Renault, M. The Fibonacci Sequence Under Various Moduli” Master’s Thesis. Wake Forest University. 1996
  12. Cahill, N.D.; D’Errico, J.R.; Narayan, D.A.; Narayan, J.Y. Fibonacci determinats. College Mathematics Journal. 2002; 3(3), 221-225