Here we solve the following system of difference equations

$$ x^{(j)}_{n+1}=\frac{F_{m+2}+F_{m+1}x^{((j+1)mod(p))}_{n-k}}{F_{m+3} +F_{m+2}x^{((j+1)mod(p))}_{n-k}},\quad n,m, p, k \in N_0, j=\overline{1,p}, $$

where \(\left( F_{n}\right) _{n=0}^{+\infty }\) is the Fibonacci sequence. We give a representation of its general solution in terms of Fibonacci numbers and the initial values. Some theoretical justifications related to the representation for the general solution are also given.

中文翻译：

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差分方程组及其表示的一般解

在这里，我们解决以下差分方程组

$$ x ^ {（（j）} _ {n + 1} = \ frac {F_ {m + 2} + F_ {m + 1} x ^ {（（（j + 1）mod（p））} _ {nk }} {F_ {m + 3} + F_ {m + 2} x ^ {（（（j + 1）mod（p））} _ {nk}}，\ quad n，m，p，k \ in N_0， j = \ overline {1，p}，$$

其中\（\ left（F_ {n} \ right）_ {n = 0} ^ {+ \ infty} \）是斐波那契数列。我们用斐波那契数和初始值来表示其一般解。还给出了与一般解表示有关的一些理论依据。