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Download PDFABSTRACT.
In this paper, we get the form of the solutions of the following difference equation systems of order four
\[
z_{n+1} = \frac{z_{n}w_{n-2}}{\,w_{n-2} + w_{n-3}\,},
\qquad
w_{n+1} = \frac{w_{n}z_{n-2}}{\,\pm z_{n-2} \pm z_{n-3}\,},
\]
where the initial conditions \( z_{-3}, z_{-2}, z_{-1}, z_{0}, w_{-3}, w_{-2}, w_{-1}, w_{0} \) are arbitrary non-zero real numbers.
