Solve the equation $x^{2}+y^{2}=x+y+2$ in integers.

#
Let's write the equation as $(2 x-1)^{2}+(2 y-1)^{2}=10$.

From this, it is clear that one term equals 9, and the other equals 1.

## Answer

$\{2,0\},\{2,1\},\{-1,0\},\{-1,1\}$.