求方程xy-x-y=42的整数解

xy-x-y+1=42+1
(x-1)(y-1)=43
43是质数
所以43=1*43=(-1)*(-43)

所以x-1=43,y-1=1
x-1=1,y-1=43
x-1=-43,y-1=-1
x-1=-1,y-1=-43

所以
x=44,y=2
x=2,y=44
x=-42,y=0
x=0,y=-42

xy-x-y=42
x(y-1)-(y-1)=43
(y-1)(x-1)=43=1x43=-1x(-43)
所以有:
y-1=1
x-1=43
解得:y=2,x=44
y-1=-1
x-1=-43
解得:y=0,x=-42
y-1=43
x-1=1
解得:y=44.x=2
y-1=-43
x-1=-1
解得:y=-42,x=0

x=2,y=44