SOME JACOBSTHAL AND JACOBSTHAL-LUCAS IDENTITIES BY MATRIX APPROACH AND THEIR APPLICATIONS

  • Piyanut Puangjumpa Department of Mathematics and Statistics, Faculty of Science and Technology, Surindra Rajabhat University, Surin 32000, Thailand https://orcid.org/0000-0001-9741-9323
  • Sa-at Muangchan Department of Mathematics and Statistics, Faculty of Science and Technology, Sakon Nakhon Rajabhat University, Sakon Nakhon 47000, Thailand
Keywords: Jacobsthal numbers, Jacobsthal-Lucas numbers, Diophantine equations, Binet’s formula

Abstract

In this research, we studied and found some identities involving Jocobsthal and Jocobsthal-Lucas numbers by using matrix approach. In the applications, we got the solutions of some Diophantine equations by applying these identities.

References

Bergum, G. E., Bennett, L., Horadam, A. F. & Moore S. D. (1985). Jacobsthal polynomials and a conjecture concerning Fibonacci-like matrices. The Fibonacci Quarterly. 23, 240 - 248.

Horadam, A. F. (1988). Jacobsthal and Pell. The Fibonacci Quarterly. 26, 79 - 83.

Horadam, A. F. (1988). Jacobsthal representation numbers. The Fibonacci Quarterly. 34, 40 - 54.

Koken, F. & Bozkurt, D. (2008) On the Jacobsthal-Lucas Numbers by Matrix Method. Int. J. Contemp. Math Sciences. 3, 1629 - 1633.

Sloane, N. (1964). The On-Line Encyclopedia of Integer Sequences (OEIS). Retrieve March 2, 2019, from https://oeis.org/. accessed 1 March 2018.

Srisawat, S., Sriprad, W. & Sthityanak, O. (2015). On the k-Jacobsthal numbers by matrix methods. Science and Technol. RMUTT J. 5(1), 70 - 76.

Srisawat, S. & Sriprad, W. (2016). Some Pell and Pell-Lucas identities by matrix methods and their applications. Science and Technol. RMUTT J. 6(1), 170 - 174.

Suvarnamani, A. (2017). Some identities of (p, q) -Fibonacci numbers by using matrix methods. PRRJ. Science and Technol. 12(2), 49 - 53.
Published
2019-01-10
Section
บทความวิจัย (Research Article)