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

Year 2017, Volume: 13 Issue: 1, 165 - 169, 30.03.2017

Yasemin Taşyurdu , Zülküf Dilmen

https://doi.org/10.18466/cbayarfbe.302663

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.

Keywords

Fibonacci Sequence Finite Ring Period

References

  • 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.

Year 2017, Volume: 13 Issue: 1, 165 - 169, 30.03.2017

Yasemin Taşyurdu , Zülküf Dilmen

https://doi.org/10.18466/cbayarfbe.302663

Abstract

References

  • 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.
There are 1 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Yasemin Taşyurdu

Zülküf Dilmen This is me

Publication Date March 30, 2017
Published in Issue Year 2017 Volume: 13 Issue: 1

Cite

APA Taşyurdu, Y., & Dilmen, Z. (2017). On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, 13(1), 165-169. https://doi.org/10.18466/cbayarfbe.302663
AMA Taşyurdu Y, Dilmen Z. On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. CBUJOS. March 2017;13(1):165-169. doi:10.18466/cbayarfbe.302663
Chicago Taşyurdu, Yasemin, and Zülküf Dilmen. “On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 13, no. 1 (March 2017): 165-69. https://doi.org/10.18466/cbayarfbe.302663.
EndNote Taşyurdu Y, Dilmen Z (March 1, 2017) On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 13 1 165–169.
IEEE Y. Taşyurdu and Z. Dilmen, “On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix”, CBUJOS, vol. 13, no. 1, pp. 165–169, 2017, doi: 10.18466/cbayarfbe.302663.
ISNAD Taşyurdu, Yasemin - Dilmen, Zülküf. “On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 13/1 (March 2017), 165-169. https://doi.org/10.18466/cbayarfbe.302663.
JAMA Taşyurdu Y, Dilmen Z. On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. CBUJOS. 2017;13:165–169.
MLA Taşyurdu, Yasemin and Zülküf Dilmen. “On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, vol. 13, no. 1, 2017, pp. 165-9, doi:10.18466/cbayarfbe.302663.
Vancouver Taşyurdu Y, Dilmen Z. On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix. CBUJOS. 2017;13(1):165-9.