求方程：xy-x-y=2的所有整数解

xy-x-y=2 xy-x-y+1=3 x(y-1)-(y-1)=3 (x-1)(y-1)=3 (x-1)=3 x=4 (x-1)=1 x=2 (y-1)=1 y=2 (y-1)=3 y=4 (x-1)=-3 x=-2 (x-1)=-1 x=0 (y-1)=-1 y=0 (y-1)=-3 y=-2 所以共有4组整数解