Abstract
We deal with the solutions of the systems of the difference equations x(n+1) = 1/x(n-p)y(n-p), y(n+1) = x(n-p)y(n-p)/x(n-q)y(n-q), and x(n+1) = 1/x(n-p)y(n-p)z(n-p), y(n+1) = x(n-p)y(n-p)z(n-p)/x(n-q)y(n-q)z(n-q), z(n+1) = x(n-q)y(n-q)z(n-q)/x(n-r)y(n-r)z(n-r), with a nonzero real numbers initial conditions. Also, the periodicity of the general system of k variables will be considered.