Question 40
Out of three expressions $\frac{x}{y}$, $\frac{x^2+x}{y^2+y}$ and $\frac{x^2+2}{y^2+2}$, for some integer $x, y$ all three are defined, two take the same integer value, and the remaining one takes a different integer value. For which pairs of integers $x, y$ is this possible?
(Bohdan Rublyov)
(Bohdan Rublyov)