Problem 1. Determine the numbers of the form $\overline{a b c}$ that satisfy the relation

$$
b \cdot \overline{a c}=c \cdot \overline{a b}+10
$$
Solution. The relation from the hypothesis comes down to $b(10 a+c)=c(10 a+b)+10 \Leftrightarrow a b=a c+1$. . $3 \mathbf{p}$

![](https://cdn.mathpix.com/cropped/2024_06_07_3347072e375db9e37c4cg-2.jpg?height=60&width=1629&top_left_y=653&top_left_x=237)
The numbers sought are 110, 121, 132, 143, 154, 165, 176, 187, $198 \ldots \ldots \ldots \ldots \ldots . \ldots 2$ p