SavedAdd your journal

Journals / Celal Bayar Üniversitesi Fen Bilimleri Dergisi / 2026 / Cilt: 13 Sayı: 1

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

Yasemin Taşyurdu
Zülküf Dilmen
Pages
165–169
Publication Date
2017-03-30
🏛️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)

It was seen that order of cyclic group generated with matrix R = a b 1 0   is equal to the period of this sequence where a , b  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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, F n  Fibonacci sequence was defined over an arbitrary ring and its some properties are investigated.
📊
Key Findings & Data:The terms of this sequence are derivated by Tridiagonal determinant of the matrix.
💡
Conclusion & Impact:It was seen that order of cyclic group generated with matrix R = a b 1 0   is equal to the period of this sequence where a , b  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.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Fibonacci Sequence · Finite Ring · Period

Abstract

In this study, F n  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 m  coefficient and exponent of each Fibonacci sequence in arbitrary rings is periodic. It was seen that order of cyclic group generated with matrix R = a b 1 0   is equal to the period of this sequence where a , b  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.

🔖

Cite This Article

Taşyurdu, Y., Dilmen, Z. (2017). 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://doi.org/10.18466/cbayarfbe.302663

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (1)

  1. 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.