2. Find all pairs of integers $(x, y)$ that satisfy the equation $x y=20-3 x+y$. For each found pair $(x, y)$, calculate the product $x y$. In the answer, write the sum of these products.
Solution. $\quad x y=20-3 x+y, \quad x y=17+3(1-x)+y, \quad(x-1) y+3(x-1)=17$, $(x-1)(y+3)=17$. Since x and y are integers, we have four cases:

1) $\left\{\begin{array}{c}y+3=17, \\ x-1=1,\end{array} \Leftrightarrow\left\{\begin{array}{c}y=14 \\ x=2\end{array}\right.\right.$
2) $\left\{\begin{array}{c}y+3=-17, \\ x-1=-1,\end{array} \Leftrightarrow\left\{\begin{array}{c}y=-20 \\ x=0\end{array}\right.\right.$
3) $\left\{\begin{array}{c}y+3=1, \\ x-1=17,\end{array} \Leftrightarrow\left\{\begin{array}{l}y=-2 \\ x=18\end{array}\right.\right.$
4) $\left\{\begin{array}{c}y+3=-1, \\ x-1=-17,\end{array} \Leftrightarrow\left\{\begin{array}{c}y=-4 \\ x=16\end{array}\right.\right.$

Answer: 56.