In this paper we show that the following four-dimensional system of difference equations xn+1=ynαzn−1β,yn+1=znγtn−1δ,zn+1=tnϵxn−1μ,tn+1=xnξyn−1ρ,n∈N0,$$\begin{array}{} \displaystyle x_{n+1}=y_{n}^{\alpha}z_{n-1}^{\beta}, \quad y_{n+1}=z_{n}^{\gamma}t_{n-1}^{\delta}, \quad z_{n+1}=t_{n}^{\epsilon}x_{n-1}^{\mu}, \quad t_{n+1}=x_{n}^{\xi}y_{n-1}^{\rho}, \qquad n\in \mathbb{N}_{0}, \end{array}$$ where the parameters α, β, γ, δ, ϵ, μ, ξ, ρ ∈ ℤ and the initial values x–i, y–i, z–i, t–i, i ∈ {0, 1}, are real numbers, can be solved in closed forms, extending further some results in literature.
本文证明了以下四维差分方程组 x n + 1 = y n α z n - 1 β , y n + 1 = z n γ t n - 1 δ , z n + 1 = t n ϵ x n - 1 μ , t n + 1 = x n ξ y n - 1 ρ , n∈ N 0 , $$\begin{array}{}\displaystyle x_{n+1}=y_{n}^{\alpha}z_{n-1}^{\beta}, \quad y_{n+1}=z_{n}^{\gamma}t_{n-1}^{\delta},\quad z_{n+1}=t_{n}^{\epsilon}x_{n-1}^{\mu}, \quad t_{n+1}=x_{n}^{\xi}y_{n-1}^{\rho}, \qquad n\in \mathbb{N}_{0}、\end{array}$$ 其中参数 α, β, γ, δ, ϵ, μ, ξ, ρ∈ ℤ 和初始值 x -i , y -i , z -i , t -i , i∈ {0, 1} 均为实数，可以用封闭形式求解，进一步扩展了文献中的一些结果。
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Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc. The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.
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