2008 USAMO 第 1 题

Prove that for each positive integer $n$, there are pairwise relatively prime integers $k_0, k_1 \dotsc, k_n$, all strictly greater than 1, such that $k_0 k_1 \dotsm k_n -1$ is the product of two consecutive integers.

证明对于每个正整数$n$，存在成对互质整数$k_0, k_1 \dotsc, k_n$，全部严格大于1，使得$k_0 k_1 \dotsm k_n -1$ 是两个连续整数的乘积。