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JACOBSTHAL FAMILY MODULO m

Year 2016, Volume: 6 Issue: 1, 15 - 21, 01.06.2016

Abstract

In this study, we investigate sets of remainder of the Jacobsthal and JacobsthalLucas numbers modulo m for some positive integers m. Also some properties related to these sets and a new method to calculate the length of period modulo m is given.

References

  • Djordjevic,G.B., (2007), Mixed convolutions of the Jacobsthal type, Applied Mathematics and Com- putation 186, pp. 646-651.
  • Falcon,F. and Plaza,A., (2009), k-Fibonacci sequences modulo m, Chaos, Solitons and Fractals 41, pp. 497-504.
  • Frey,D.D. and Sellers,J.A., (2000), Jacobsthal numbers and alternating sign matrices, Journal of Integer Sequences 3, article 00.2.3.
  • Fulton,J.D. and Morris,W.L., (1969/1970), On arithmetical functions related to the Fibonacci numbers, Acta Arithmetica 16, pp. 105-110.
  • Guo,C. and Koch,A., (2009), Bounds for Fibonacci period growth, Involve A Journal of Mathematics 2.
  • Horadam,A.F., (1996), Jacobsthal representation numbers, Fibonacci Quarterly 34, pp. 40-54.
  • Koshy,T., (2001), Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc, NY.
  • Renault,M., (1996), Properties of the Fibonacci sequence under various moduli, Master’s thesis, Wake Forest University.
  • Wall,D.D., (1960), Fibonacci series modulo m, Amer. Math. Monthly 67, pp. 525-532.
Year 2016, Volume: 6 Issue: 1, 15 - 21, 01.06.2016

Abstract

References

  • Djordjevic,G.B., (2007), Mixed convolutions of the Jacobsthal type, Applied Mathematics and Com- putation 186, pp. 646-651.
  • Falcon,F. and Plaza,A., (2009), k-Fibonacci sequences modulo m, Chaos, Solitons and Fractals 41, pp. 497-504.
  • Frey,D.D. and Sellers,J.A., (2000), Jacobsthal numbers and alternating sign matrices, Journal of Integer Sequences 3, article 00.2.3.
  • Fulton,J.D. and Morris,W.L., (1969/1970), On arithmetical functions related to the Fibonacci numbers, Acta Arithmetica 16, pp. 105-110.
  • Guo,C. and Koch,A., (2009), Bounds for Fibonacci period growth, Involve A Journal of Mathematics 2.
  • Horadam,A.F., (1996), Jacobsthal representation numbers, Fibonacci Quarterly 34, pp. 40-54.
  • Koshy,T., (2001), Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc, NY.
  • Renault,M., (1996), Properties of the Fibonacci sequence under various moduli, Master’s thesis, Wake Forest University.
  • Wall,D.D., (1960), Fibonacci series modulo m, Amer. Math. Monthly 67, pp. 525-532.
There are 9 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Y. Yazlık This is me

N. Yılmaz

N. Taskara This is me

K. Uslu This is me

Publication Date June 1, 2016
Published in Issue Year 2016 Volume: 6 Issue: 1

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