Question 9
Find the smallest integer $m$ for which there are positive integers $n \gt k \gt 1$ satisfying the equation
$$
\underbrace{11 \ldots 1}_{n} = \underbrace{11 \ldots 1}_{k} \cdot m.
$$
$$
\underbrace{11 \ldots 1}_{n} = \underbrace{11 \ldots 1}_{k} \cdot m.
$$