** Authors:**
YACINE HALIM, MASSAOUD BERKAL, AMIRA KHELIFA

** Abstract: **
In this paper we solve the following system of difference equations
\begin{equation*}
x_{n+1}=\dfrac{z_{n-1}}{a+by_nz_{n-1}},\quad
y_{n+1}=\dfrac{x_{n-1}}{a+bz_nx_{n-1}},\quad
z_{n+1}=\dfrac{y_{n-1}}{a+bx_ny_{n-1}},\quad n\in \mathbb{N}_{0}
\end{equation*}
where parameters $a, b$ and initial values $x_{-1},x_{0},y_{-1},y_{0},z_{-1},z_{0}$ are nonzero real numbers,
and give a representation of its general solution in terms of a specially chosen solutions
to homogeneous linear difference equation with constant coefficients associated to
the system.

** Keywords: **
System of difference equations, general solution, representation of solutions

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