1981 IMO 第 1 题

${ }^{\mathrm{IMO} 4}$ (a) For which values of $n>2$ is there a set of $n$ consecutive positive integers such that the largest number in the set is a divisor of the least common multiple of the remaining $n-1$ numbers? (b) For which values of $n>2$ is there a unique set having the stated property?

${ }^{\mathrm{IMO} 4}$ (a) 对于 $n>2$ 的哪个值，存在一组 $n$ 个连续正整数，使得该组中最大的数是其余 $n-1$ 数的最小公倍数的约数？ (b) 对于 $n>2$ 的哪些值，存在具有指定属性的唯一集合？