On the solutions of a general system of difference equations (Q444305)

Summary: 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.