Question 145
If $a$ and $b$ are positive integers, then $\overline{a.b}$ is the decimal number obtained by writing the number $a$, then the decimal point and then the number $b$. For example, if $a = 20$ and $b = 17$, then $\overline{a.b} = 20.17$ and $\overline{b.a} = 17.2$.
Determine all pairs $(a, b)$ of positive integers such that $\overline{a.b} \cdot \overline{b.a} = 13$.
Determine all pairs $(a, b)$ of positive integers such that $\overline{a.b} \cdot \overline{b.a} = 13$.