5. Determine how many integer solutions \((x, y)\) the equation

$$
y^{3}+x^{2} y+2 x y^{2}+x^{2}+3 x y+2 y^{2}+3 x+y+2=0
$$

has, for which \(|x| \leqslant 20\) and \(|y| \leqslant 18\).

## SOLUTIONS TO THE MUNICIPAL COMPETITION IN MATHEMATICS FOR HIGH SCHOOL STUDENTS, 13. 1. 2018.

## First Grade - A Category