MMN-4315

# Connection of Balancing numbers with solution of a system of two higher-order difference equations

*Yacine Halim*;

*Amira Khelifa*;

*Niâma Mokrani*;

## Abstract

We provide some theoretical justifications pertaining to the representation for the solution
of the system of the higher-order rational difference
equations
\begin{equation*}
x_{n+1}=\frac{1}{6-y_{n-k}},\quad
y_{n+1}=\frac{1}{6-x_{n-k}},\qquad n, k\in \mathbb{N}_0.
\end{equation*}
where $\mathbb{N}_{0}=\mathbb{N}\cup \left\{0\right\}$, and the initial
conditions $x_{-k}$, $x_{-k+1},\ldots$, $x_{0}$, $y_{-k}$,
$y_{-k+1},\ldots$, $y_{0}$ are non zero real numbers such
that their solution is related to Balancing numbers.
We also study the stability character and asymptotic behavior
of this system.

Vol. 24 (2023), No. 2, pp. 779-788