1994 IMO 第 1 题

A1 (USA) 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 $a_{n}$, $0 \leq n \leq 998$.

A1 (美国) 对于每个非负整数 $n$，令 $a_{0}=1994$ 和 $a_{n+1}=\frac{a_{n}^{2}}{a_{n}+1}$ 。证明$1994-n$是小于或等于$a_{n}$,$0\leq n\leq 998$的最大整数。