2001 IMO Shortlist S05

Find all positive integers $a_1, a_2, \ldots, a_n$ such that

$$

\frac{99}{100} = \frac{a_0}{a_1} + \frac{a_1}{a_2} + \cdots +

\frac{a_{n-1}}{a_n},

$$

where $a_0 = 1$ and $(a_{k+1}-1)a_{k-1} \geq a_k^2(a_k - 1)$ for $k = 1,2,\ldots,n-1$ .

找到所有正整数 $a_1, a_2, \ldots, a_n$ 使得

$$

\frac{99}{100} = \frac{a_0}{a_1} + \frac{a_1}{a_2} + \cdots +

\frac{a_{n-1}}{a_n},

$$

其中 $a_0 = 1$ 和 $(a_{k+1}-1)a_{k-1} \geq a_k^2(a_k - 1)$ 对于 $k = 1,2,\ldots,n-1$ 。