Research ArticleNo Access

Representation of integers by $k$ $k$ -generalized Fibonacci sequences and applications in cryptography

Salim Badidja

Kasdi Merbah University, Ouargla, BP 30000, Algeria

E-mail Address: badidja@hotmail.fr

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Ahmed Ait Mokhtar

Height Normal School, Kouba, Algiers, BP 92, Algeria

E-mail Address: ahmed.aitmokhtar@yahoo.fr

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, and

Özen Özer

Department of Mathematics, Faculty of Science and Arts, Kırklareli University, Kırklareli-39100, Turkey

E-mail Address: ozenozer39@gmail.com

Corresponding author.

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https://doi.org/10.1142/S1793557121501576Cited by:1 (Source: Crossref)

Abstract

The aim of this paper is to construct a relation between tribonacci numbers and generalized tribonacci numbers. Besides, certain conditions are obtained to generalize the representation of a positive integer $N$ $N$ which is determined in [S. Badidja and A. Boudaoud, Representation of positive integers as a sum of distinct tribonacci numbers, J. Math. Statistic. 13 (2017) 57–61] for a $k$ $k$ -generalized Fibonacci numbers ${(F_{n}^{(k)})}_{n \in ℕ^{*}}$ . Lastly, some applications to cryptography are given by using ${(F_{n}^{(k)})}_{n \in ℕ^{*}}$ .

Communicated by B. K. Dass

Keywords:

AMSC: 11B39, 11B83

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