## Task 16/64

Which two-digit numbers satisfy the following condition: The product of the two digits, decreased by their sum, is 3?
If we denote the sought number by $u=10 x+y$ (where $x$ and $y$ are integers with $0 \leq x \leq 9,0 \leq y \leq 9$), then the given condition leads to the equation

$$
x y-(x+y)=3
$$

By rearranging, we obtain the equations

$$
y(x-1)=x+3 \rightarrow y=\frac{x+3}{x-1} \rightarrow y=1+\frac{4}{x-1}
$$

Since $y$ is an integer, $(x-1)$ must be a divisor of 4. Therefore, the following values are possible

| $x-1:$ | 1 | 2 | 4 |
| :---: | :---: | :---: | :---: |
| $x:$ | 2 | 3 | 5 |
| $y:$ | 5 | 3 | 2 |

Thus, the numbers are $u_{1}=25, u_{2}=33$, and $u_{3}=52$.