PISANO PERIODS FOR THE k-FIBONACCI AND k-LUCAS SEQUENCES MOD 2ⁿ
Abstract
The
goal of this paper is to investigate period of
k-Lucas sequence with related divisibility
properties, and periods of k- Fibonacci and k-Lucas sequences mod 2n .
Keywords
References
- Bolat, C. and Köse, H., “On the Properties of k-Fibonacci Numbers”, Int J.Contemp.Math.Sciences, 22: 1097-1105, (2010).
- Falcon, S. and Plaza, A., “On the Fibonacci k-numbers”, Chaos, Solutions and Fractals, 32: 1615-1624, (2007).
- Falcon, S. and Plaza, A., “k-Fibonacci Sequences Modulo m”, Chaos, Solutions and Fractals, 41: 497-504, (2009).
- Falcon, S., “On the k-Lucas Numbers”, Int J.Contemp.Math.Sciences, 21: 1039-1050, (2011).
- Falcon, S. and Plaza, A., “The k-Fibonacci Sequences and the Pascal 2-triangle”, Chaos, Solutions and Fractals, 33: 38-49, (2007).
- Falcon, S. and Plaza, A., “On k-Fibonacci Sequences and Polynomials and their Derivatives”, Chaos, Solutions and Fractals, 39: 1005-1019, (2007).
- Kramer, J., Hoggat, V.E., “Special Cases of Fibonacci Periodicity”, 1972.
- Niven, I., Zuckerman, H.S.,Montegomery, H.L., “An Introduction to the Theory of Numbers”, 5 nd ed., John Wiley Sons, Inc., 1991.
Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Authors
Gül Özkan Kızılırmak
Dursun TAŞCI
Türkiye
Publication Date
March 1, 2018
Submission Date
April 10, 2017
Acceptance Date
December 23, 2017
Published in Issue
Year 2018 Volume: 31 Number: 1