Task 2. Determine all digits $a, b$ for which the number $\overline{a 13 b}$ is divisible by 45.
Solution. The number $\overline{a 13 b}$ is divisible by 45 if it is divisible by 9 and 5. This means the digit $b$ can be 0 or 5. If $b=0$, then $\overline{a 130}$ is divisible by 9 if $a+1+3+0=a+4$ is divisible by 9 and $a=5$, so the desired number is 5130. If, however, $b=5$, then $\overline{a 135}$ is divisible by 9 if $a+1+3+5=a+9$. But $a \neq 0$, so $a=9$, i.e., the desired number is 9135.