17. Find the digits $a$ and $b$ in the number $\overline{42 a 4 b}$, given that this number is divisible by 72.
17. If a number is divisible by 72, then it is divisible by 9 and 8. Since $4+2+4=10$, then $a+b=8$ or $a+b=17$. If $a+b=17$, then either $a=9$ and $b=8$, or $a=8$ and $b=9$. But in both cases, the resulting numbers are not divisible by 8. Therefore, $a+b=8$. Based on divisibility by 8, only $a=8$ and $b=0$, or $a=0$ and $b=8$ are possible. Indeed, $42840: 72=595, 42048: 72=584$. We have the solutions: 1) $a=8, b=0 ; 2$ ) $a=0, b=8$.