Question 170
Let $a$ and $b$ be two nonzero digits, not necessarily different. The two-digit number $\overline{a b}$ is called curious if it is a divisor of the number $\overline{b a}$, which is formed by swapping the order of the digits of $\overline{a b}$. Find all curious numbers.
Remark: The bar over the numbers serves to distinguish the product $a \cdot b$ from the two-digit number $\overline{a b}$.
Remark: The bar over the numbers serves to distinguish the product $a \cdot b$ from the two-digit number $\overline{a b}$.