2004 IMO 第 2 题

A2 (ROM) An infinite sequence $a_{0}, a_{1}, a_{2}, \ldots$ of real numbers satisfies the condition $$a_{n}=\left|a_{n+1}-a_{n+2}\right| \text { for every } n \geq 0$$ with $a_{0}$ and $a_{1}$ positive and distinct. Can this sequence be bounded?

A2 (ROM) 实数的无限序列 $a_{0}, a_{1}, a_{2}, \ldots$ 满足条件 $$a_{n}=\left|a_{n+1}-a_{n+2}\right| \text { 对于每个 } n \geq 0$$，其中 $a_{0}$ 和 $a_{1}$ 为正且不同。这个序列可以有界吗？