Question 22
$m$ and $n$ are relatively prime positive integers. The interval $[0, 1]$ is divided into $m + n$ equal subintervals. Show that each part except those at each end contains just one of the numbers $1/m$, $2/m$, $3/m$, $\ldots$, $(m-1)/m$, $1/n$, $2/n$, $\ldots$, $(n-1)/n$.