JACOBSTHAL FAMILY MODULO m

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

Y. Yazlık N. Yılmaz N. Taskara K. Uslu

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.

Keywords

Jacobsthal numbers, Jacobsthal-Lucas numbers, modulo, period.

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.