MMN-3385

# On the solutions of a system of (2p+1) difference equations of higher order

*A. Khelifa*;

*Y. Halim*;

*M. Berkal*;

## Abstract

In this paper we represents the well-defined solutions of the system of the
higher-order rational difference equations
\begin{equation*}
x^{(j)}_{n+1}=\dfrac{1+2x^{(j+1)mod(2p+1)}_{n-k}}{3+x^{(j+1)mod(2p+1)}_{n-k}},\quad n, k, p \in \mathbb{N}_{0}
\end{equation*}
in terms of Fibonacci and Lucase sequences, where the initial values
$x^{(j)}_{-k}, x^{(j)}_{-k+1}$,\\$\ldots, x^{(-1)}_0$ and $x^{(i)}_0$, $j=1,2,\ldots,2p+1$, do not equal -3. Some theoretical explanations related to the representation for the general solution
are also given.

Vol. 22 (2021), No. 1, pp. 331-350