3. Determine all natural numbers of the form $\overline{a b c}$ which, when divided by $\overline{b c}$, give a quotient of 4 and a remainder of $\overline{b c}-8$.

Gazeta Matematică - nr.10/ 2012
3. $\overline{a b c}=\overline{b c} \cdot 4+\overline{b c}-8, a, b \neq 0$.

$100 a+\overline{b c}=5 \overline{b c}-8$

$100 a=4 \overline{b c}-8 /: 4$

$25 a=\overline{b c}-2$

We observe that $\overline{b c}-2 \leq 97 \Rightarrow a \leq 3$.

For: $a=3 \Rightarrow \overline{b c}=79$

$$
\begin{aligned}
& a=2 \Rightarrow \overline{b c}=52 \\
& a=1 \Rightarrow \overline{b c}=27
\end{aligned}
$$