Let $x$ and $y$ be the pair to be found, then $x+y=xy$. That is, $(x-1)(y-1)=1$.


Because $x, y$ are integers. So $x-1=1, y-1=1$ or $x-1=-1, y-1=1$, i.e., $x=2$, $y=2$ or $x=y=0$.
Therefore, the integer pairs that satisfy the condition are $(2,2),(0,0)$.