VN-TST 1996 Problem 6

Find all reals $a$ such that the sequence $\{x(n)\}$ , $n=0,1,2, \ldots$ that satisfy: $x(0)=1996$ and $x_{n+1} = \frac{a}{1+x(n)^2}$ for any natural number $n$ has a limit as n goes to infinity.