## Problem 1

$\overline{a b c}=\overline{b c} \cdot 4+\sqrt{b c}-8 \quad$ (1p)

$100 \mathrm{a}+\overline{b c}=\overline{b c} \cdot 4+\overline{b c}-8$ (1p)

$25 \mathrm{a}=\Xi_{c}-2$ (1p)

$\mathrm{a} \in\{1,2,3\}$ (1p)

$\mathrm{a}=1 \Rightarrow \overline{\sigma c}=27 \Rightarrow \overline{a b c}=127$ (1p)

$\mathrm{a}=2 \Rightarrow \overline{b c}=52 \Rightarrow \overline{a b c}=252$ (1p)

$\mathrm{a}=3 \Rightarrow \overline{b c}=77 \Rightarrow \overline{a b c}=377$ (1p)
## Problem 1

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 $\overline{b c}-8$.