Some Identities of Fibonacci-Like Based on Lucas Numbers

Ulfa Hasanah; Sri Gemawati; Syamsudhuha

doi:https://doi.org/10.14445/22315373/IJMTT-V65I2P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 2 | Year 2019 | Article Id. IJMTT-V65I2P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I2P508

Some Identities of Fibonacci-Like Based on Lucas Numbers

Ulfa Hasanah, Sri Gemawati, Syamsudhuha

Abstract

In this paper, we determine some identities of Fibonacci-Like number based on Lucas number then Fibonacci-Like is just defined by Lucas number. The new identities of Fibonacci-Like can be proved by Binet’s formula.

Keywords

Fibonacci, Fibonacci-Like, Lucas, Binet’s formula

References

[1] D.M. Burton, Elementary Number Theory, Allyn & Bacon Inc., Boston, (2011).
[2] B. Demirturk and R. Keskin, Integer solutions of some diophantine equations via Fibonacci and Lucas number, Journal of Integer Sequence, 12 (2009), 1–14.
[3] V. E. Hoggat and A. E Meder, Fibonacci and Lucas Numbers, Houghton Mifflin Company, Boston, (1969).
[4] Y. K. Gupta, O. Sikhwal, dan M. Singh, Determinantal Identities of Fibonacci, Lucas and Generalized Fibonacci-Lucas Sequence, MAYFEB Journal of Mathematics, 2 (2016), 17–23.
[5] T. Koshy, Elementary Number Theory with Applications Second Edition, Elsevier Academic Press, London, (2007).
[6] T. Koshy, Fibonacci and Lucas Number with Applications, Wiley–Interscience, New York, (2001). D. M. Mahajan, The Binet Forms for the Fibonacci and Lucas Number, International Journal of Mathematics Trend and Technology , 10 (2014), 14–16.
[7] G. P. S. Rathore, O. Sikhwal and R. Choudhary, Generalized Fibonacci- Like Sequence and Some Identities, SCIREA Journal of Mathematics, 1 (2016), 107–118.
[8] K. H. Rosen, Discrete Mathematics and Its Applications Seventh Edition, McGraw–Hill Companies, New York, (2012).
[9] B.Singh, P. Bhadouria and O. Sikhwai, Fibonacci-Like Sequence and its Properties, Int. J. Contemp. Math. Sciences, 5 (2010), 859–868.
[10] B.Singh, P. Bhadouria and O. Sikhwai, Generalized Identities Involving Common Factors of Fibonacci and Lucas Number, International Journal of Algebra, 5 (2011), 637–645.
[11] A. Suvarnamani and M. Tatong, Some Properties of The Product of (p, q) Fibonacci and (p, q)- Lucas Number, International Journal of GEOMATE, 13(2017), 16–19.

Citation :

Ulfa Hasanah, Sri Gemawati, Syamsudhuha, "Some Identities of Fibonacci-Like Based on Lucas Numbers," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 2, pp. 37-40, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I2P508