ISL 1994 A1

Let $a_{0} = 1994$ and $a_{n + 1} = \frac {a_{n}^{2}}{a_{n} + 1}$ for each nonnegative integer $n$ . Prove that $1994 - n$ is the greatest integer less than or equal to $a_{n}$ , $0 \leq n \leq 998$