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

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 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-generalized Fibonacci numbers (Fn(k)) n is an element of N*. Lastly, some applications to cryptography are given by using (Fn(k)) n is an element of N*.