International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

A Congruent Property of Gibonacci Number Modulo Prime

  • Wipawee Tangjai1*
  • Kodchaphon Wanichang
  • Montathip Srikao
  • Punyanuch Kheawkrai
  1. a:1:{s:5:"en_US";s:23:"Mahasarakham University";}

* Corresponding author

Abstract

Let a, b ∈ Z and p be a prime number such that a and b are not divisible by p. In this work, we give a congruent property modulo a prime number p of the gibonacci number defined by Gn = Gn−1 + Gn−2 with initial condition G1 = a, G2 = b. We show that a the gibonacci sequence satisfying Gkp−(p/5) ≡ Gk−1 (mod p) for all positive integer k and such odd prime p ≠ 5 if and only if a ≡ b (mod p). Moreover, for each odd prime number p, we give a necessary and sufficient condition yielding Gkp−(p/5) ≡ Gk−1 (mod p). We also find a relation between the sequences in the same equivalent class in modulo 5 constructed by Aoki and Sakai [1] that leads to such congruent property.

How to Cite

W. Tangjai, K. Wanichang, M. Srikao, P. Kheawkrai, A Congruent Property of Gibonacci Number Modulo Prime, Int. J. Anal. Appl. 21 (2023), 24. https://doi.org/10.28924/2291-8639-21-2023-24

BibTeX
@article{Tangjai2023,
  author  = {Tangjai, Wipawee and Wanichang, Kodchaphon and Srikao, Montathip and Kheawkrai, Punyanuch},
  title   = {A Congruent Property of Gibonacci Number Modulo Prime},
  journal = {Int. J. Anal. Appl.},
  volume  = {21},
  year    = {2023},
  pages   = {24},
  doi     = {10.28924/2291-8639-21-2023-24}
}

References

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