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

Year 2018, Volume: 31 Issue: 1, 213 - 220, 01.03.2018

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 .




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.
  • Rogers, N., Campbell, C.W., “The Period of the Fibonacci Sequence Modulo j”, Phd, The University of Arizona, Tucson, USA, 2007.
  • Vajda, S., “Fibonacci&Lucas numbers, and the Golden Section, Theory and applications, Ellis Horwood Limited, 1989.
  • Wall, D.D., “Fibonacci Series Modulo m”, The American Mathematical Monthly, 67: 525-532, (1960).
Year 2018, Volume: 31 Issue: 1, 213 - 220, 01.03.2018

Abstract

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.
  • Rogers, N., Campbell, C.W., “The Period of the Fibonacci Sequence Modulo j”, Phd, The University of Arizona, Tucson, USA, 2007.
  • Vajda, S., “Fibonacci&Lucas numbers, and the Golden Section, Theory and applications, Ellis Horwood Limited, 1989.
  • Wall, D.D., “Fibonacci Series Modulo m”, The American Mathematical Monthly, 67: 525-532, (1960).
There are 11 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Gül Özkan Kızılırmak

Publication Date March 1, 2018
Published in Issue Year 2018 Volume: 31 Issue: 1

Cite

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.
AMA Özkan Kızılırmak G. PISANO PERIODS FOR THE k-FIBONACCI AND k-LUCAS SEQUENCES MOD 2ⁿ. Gazi University Journal of Science. March 2018;31(1):213-220.
Chicago Özkan Kızılırmak, Gül. “PISANO PERIODS FOR THE K-FIBONACCI AND K-LUCAS SEQUENCES MOD 2ⁿ”. Gazi University Journal of Science 31, no. 1 (March 2018): 213-20.
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 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, 2018.
ISNAD Özkan Kızılırmak, Gül. “PISANO PERIODS FOR THE K-FIBONACCI AND K-LUCAS SEQUENCES MOD 2ⁿ”. Gazi University Journal of Science 31/1 (March 2018), 213-220.
JAMA 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, 2018, pp. 213-20.
Vancouver Özkan Kızılırmak G. PISANO PERIODS FOR THE k-FIBONACCI AND k-LUCAS SEQUENCES MOD 2ⁿ. Gazi University Journal of Science. 2018;31(1):213-20.