Question

求方程xy-10(x+y)=1

Answer 1

xy-10(x+y)=1

xy-10x-10y+100=101

(x-10)(y-10)=101

①

x-10=1

y-10=101

x=11,y=111

②

x-10=-1

y-10=-101

x=9,y=-91

整数解为:

x=11,y=111

x=111,y=11

x=-9,y=-91

x=-91,y=-9