J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 19, 2013, Number 1, Pages 66—72
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Authors and affiliations
J. V. Leyendekkers
Faculty of Science, The University of Sydney
NSW 2006, Australia
A. G. Shannon
Faculty of Engineering & IT, University of Technology
Sydney, NSW 2007, Australia
Abstract
Various Fibonacci number identities are analyzed in terms of their underlying integer structure in the modular ring Z5.
Keywords
- Fibonacci sequence
- Golden Ratio
- Modular rings
- Binet formula
AMS Classification
- 11B39
- 11B50
References
- Leyendekkers, J.V., A.G. Shannon, J.M. Rybak. 2007. Pattern Recognition: Modular Rings and Integer Structure. North Sydney: Raffles KvB Monograph No 9.
- Leyendekkers, J.V., A.G. Shannon. The Modular Ring Z5. Notes on Number Theory and Discrete Mathematics. Vol. 18, 2012, No. 2, 28–33.
- Leyendekkers, J.V., A.G. Shannon. Geometrical and Pellian Sequences. Advanced Studies in Contemporary Mathematics. Vol. 22, 2012, No. 4, 507–508.
- Leyendekkers, J.V., A.G. Shannon. On the Golden Ratio (Submitted).
- Leyendekkers, J.V., A.G. Shannon. The Decimal String of the Golden Ratio (Submitted).
- Livio, Mario. The Golden Ratio. Golden Books, New York, 2002.
- Shannon, A.G., A.F. Horadam, S.N. Collings. Some Fibonacci Congruences. The Fibonacci Quarterly. Vol. 12, 1974, No. 4, 351–354.
- Simons, C.S., M. Wright. Fibonacci Imposters. International Journal of Mathematical Education in Science and Technology. Vol. 38, 2007, No. 5, 677–682.
- Ward, M. The Algebra of Recurring Series. Annals of Mathematics. Vol. 32, 1931, No. 1, 1–9.
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Cite this paper
Leyendekkers, J., & Shannon, A. (2013). The structure of the Fibonacci numbers in the modular ring Z5. Notes on Number Theory and Discrete Mathematics, 19(1), 66-72.