Integer Pairs Satisfying x + y = xy

Rearranging the equation: $xy - x - y = 0 \implies xy - x - y + 1 = 1 \implies (x - 1)(y - 1) = 1$ Since $x, y$ are integers, $(x - 1)$ and $(y - 1)$ must be factors of $1$. Case 1: $x - 1 = 1, y - 1 = 1 \implies x = 2, y = 2$. Case 2: $x - 1 = -1, y - 1 = -1 \implies x = 0, y = 0$. So there are exactly $2$ integer pairs: $(0,0)$ and $(2,2)$.