\section*{Problem 4 - 161044}

Determine all integer pairs \((x ; y)\) that satisfy the following equation!

\[
x y + 3 x - 2 y - 3 = 0
\]
}

There can be no solution where \(x=2\), because otherwise \(0=2 y+6-2 y-3=3\).

Thus, we can equivalently transform to \(y=\frac{3-3 x}{x-2}=-3-\frac{3}{x-2}\).

For \(y\) to be an integer, \(x-2\) must be a divisor of 3. Therefore, \(x \in\{2 \pm 1,2 \pm 3\}=\{-1,1,3,5\}\).

Consequently, \((x, y)\) is an integer solution pair if and only if \((x, y) \in\{(-1,-2),(1,0),(3,-6),(5,-4)\}\).