USAMO
1988
The repeating decimal $ 0.ab \cdots k \overline {pq \cdots u} = \dfrac {m}{n} $, where $m$ and $n$ are relatively prime integers, and there is at least one decimal before the repeating part. Show that $n$ is divisible by $2$ or $5$ (or both). (For example, $ 0.011 \overline {36} = 0.01136363636 \cdots = \dfrac {1}{88} $, and $88$ is divisible by $2$.)