1988 USAMO 第 1 题

The repeating decimal $0.ab\cdots k\overline{pq\cdots u}=\frac mn$, where $m$ and $n$ are relatively prime integers, and there is at least one decimal before the repeating part. Show that $n$ is divisble by 2 or 5 (or both). (For example, $0.011\overline{36}=0.01136363636\cdots=\frac 1{88}$, and 88 is divisible by 2.)

重复小数$0.ab\cdots k\overline{pq\cdots u}=\frac mn$，其中$m$和$n$是互质整数，并且重复部分之前至少有一位小数。证明 $n$ 能被 2 或 5(或两者)整除。 (例如，$0.011\overline{36}=0.01136363636\cdots=\frac 1{88}$，并且 88 可以被 2 整除。)