Consider the three-dimensional system of difference equations xn+1 = ∏k j=0 zn−3j ∏k j=1 xn−(3j−1) ( an + bn ∏k j=0 zn−3j ), yn+1 = ∏k j=0 xn−3j ∏k j=1 yn−(3j−1) ( cn + dn ∏k j=0 xn−3j ), zn+1 = ∏k j=0 ...

It is shown that the following (k + l)-order nonlinear difference equation xn = xn−kxn−k−l xn−l (an + bnxn−kxn−k−l) , n ∈ N0, where k, l ∈ N, (an)n∈N0 , (bn)n∈N0 and the initial values x−i, i = 1, k + l, are real ...