The aim of this paper is to find formulas for the solutions of the nonlinear system of difference equations related to symmetry Pn+1 = TnTn−2 −Pn−3−Tn , Tn+1 = PnPn−2 ±Tn−3±Pn , where the initial conditions P−3, P−2, P−1, P0, T−3, T−2, T−1, and T0 are arbitrary real numbers. Moreover, the theoretical results are verified through several numerical examples, which are simulated and graphically illustrated using mathematical programs.
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