The article deals with the equation
where are nonnegative reals, nonnegative integers, . Equation (1) has a zero equilibrium point and, if , a nonzero equilibrium point . The main results are the following: If then the zero is a locally asymptotic stable equilibrium point; if then both equilibrium points are unstable. The case and is also considered; in this case there exist periodic solutions with the prime period and every solution of (1) converges to a periodic solution of (1) with the period .