xy-(x+y)=1000

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xy-(x+y)=1000
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xy-(x+y)=1000
xy-(x+y)=1000

xy-(x+y)=1000
xy-x-y+1=1001
(x-1)(y-1)=1001=7*11*13

xy-(x+y)=1000
xy-x-y=1000
x(y-1)-(y-1)-1=1000
(x-1)(y-1)=1001

二元二次方程有无数组解。其中正整数解有以下八组:
xy-(x+y)=1000
xy-x-y=1000
x(y-1)-(y-1)-1=1000
(x-1)(y-1)=1001=1*1001=7*143=11*91=13*77
x-1=1,y-1=1001 x=2,y=1002
x-1=1001,y-1=1 x=1002,y=2
...

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二元二次方程有无数组解。其中正整数解有以下八组:
xy-(x+y)=1000
xy-x-y=1000
x(y-1)-(y-1)-1=1000
(x-1)(y-1)=1001=1*1001=7*143=11*91=13*77
x-1=1,y-1=1001 x=2,y=1002
x-1=1001,y-1=1 x=1002,y=2
x-1=7,y-1=143 x=8,y=144
x-1=143,y-1=7 x=144,y=8
x-1=11,y-1=91 x=12,y=92
x-1=91,y-1=11 x=92,y=12
x-1=13,y-1=77 x=14,y=78
x-1=77,y-1=13 x=78,y=14

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无数解