Research Article

PISANO PERIODS FOR THE k-FIBONACCI AND k-LUCAS SEQUENCES MOD 2ⁿ

Volume: 31 Number: 1 March 1, 2018
EN

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

  1. Bolat, C. and Köse, H., “On the Properties of k-Fibonacci Numbers”, Int J.Contemp.Math.Sciences, 22: 1097-1105, (2010).
  2. Falcon, S. and Plaza, A., “On the Fibonacci k-numbers”, Chaos, Solutions and Fractals, 32: 1615-1624, (2007).
  3. Falcon, S. and Plaza, A., “k-Fibonacci Sequences Modulo m”, Chaos, Solutions and Fractals, 41: 497-504, (2009).
  4. Falcon, S., “On the k-Lucas Numbers”, Int J.Contemp.Math.Sciences, 21: 1039-1050, (2011).
  5. Falcon, S. and Plaza, A., “The k-Fibonacci Sequences and the Pascal 2-triangle”, Chaos, Solutions and Fractals, 33: 38-49, (2007).
  6. Falcon, S. and Plaza, A., “On k-Fibonacci Sequences and Polynomials and their Derivatives”, Chaos, Solutions and Fractals, 39: 1005-1019, (2007).
  7. Kramer, J., Hoggat, V.E., “Special Cases of Fibonacci Periodicity”, 1972.
  8. 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

APA
Özkan Kızılırmak, G. (2018). PISANO PERIODS FOR THE k-FIBONACCI AND k-LUCAS SEQUENCES MOD 2ⁿ. Gazi University Journal of Science, 31(1), 213-220. https://izlik.org/JA98KM28GY
AMA
1.Özkan Kızılırmak G. PISANO PERIODS FOR THE k-FIBONACCI AND k-LUCAS SEQUENCES MOD 2ⁿ. Gazi University Journal of Science. 2018;31(1):213-220. https://izlik.org/JA98KM28GY
Chicago
Özkan Kızılırmak, Gül. 2018. “PISANO PERIODS FOR THE K-FIBONACCI AND K-LUCAS SEQUENCES MOD 2ⁿ”. Gazi University Journal of Science 31 (1): 213-20. https://izlik.org/JA98KM28GY.
EndNote
Özkan Kızılırmak G (March 1, 2018) PISANO PERIODS FOR THE k-FIBONACCI AND k-LUCAS SEQUENCES MOD 2ⁿ. Gazi University Journal of Science 31 1 213–220.
IEEE
[1]G. Özkan Kızılırmak, “PISANO PERIODS FOR THE k-FIBONACCI AND k-LUCAS SEQUENCES MOD 2ⁿ”, Gazi University Journal of Science, vol. 31, no. 1, pp. 213–220, Mar. 2018, [Online]. Available: https://izlik.org/JA98KM28GY
ISNAD
Özkan Kızılırmak, Gül. “PISANO PERIODS FOR THE K-FIBONACCI AND K-LUCAS SEQUENCES MOD 2ⁿ”. Gazi University Journal of Science 31/1 (March 1, 2018): 213-220. https://izlik.org/JA98KM28GY.
JAMA
1.Özkan Kızılırmak G. PISANO PERIODS FOR THE k-FIBONACCI AND k-LUCAS SEQUENCES MOD 2ⁿ. Gazi University Journal of Science. 2018;31:213–220.
MLA
Özkan Kızılırmak, Gül. “PISANO PERIODS FOR THE K-FIBONACCI AND K-LUCAS SEQUENCES MOD 2ⁿ”. Gazi University Journal of Science, vol. 31, no. 1, Mar. 2018, pp. 213-20, https://izlik.org/JA98KM28GY.
Vancouver
1.Gül Özkan Kızılırmak. PISANO PERIODS FOR THE k-FIBONACCI AND k-LUCAS SEQUENCES MOD 2ⁿ. Gazi University Journal of Science [Internet]. 2018 Mar. 1;31(1):213-20. Available from: https://izlik.org/JA98KM28GY