Narrow Results

In this paper, we find all integers $c$ having at least two representations as a difference between a Fibonacci number and a Tribonacci number.

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 ${(F_n^{(k)})}_{n\in {\mathbb{N}}^{\ast }}$. Lastly, some applications to cryptography are given by using ${(F_n^{(k)})}_{n\in {\mathbb{N}}^{\ast }}$.