求xy=x+y+1的整数解

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求xy=x+y+1的整数解求xy=x+y+1的整数解求xy=x+y+1的整数解xy-x=y+1x(y-1)=y+1x=(y-1+2)/(y-1)x=1+2/(y-1)据题意,x,y均为整数,则2/(y

求xy=x+y+1的整数解
求xy=x+y+1的整数解

求xy=x+y+1的整数解
xy-x=y+1
x(y-1)=y+1
x=(y-1+2)/(y-1)
x=1+2/(y-1)
据题意,x,y均为整数,则2/(y-1)为整数
y=2或y=3或y=-1或y=0
则x=3或x=2或x=0或x=-1

x(y-1)=y+1
x=(y-1)/(y+1)
x=1-2/(y+1)
y可能的解-3 -2 0 1 对应x...
p。s x y是可以互换的

xy=x+y+1->x(y-1)=y-1+2->(x-1)(y-1)=2
所以x-1=2,y-1=1或x-1=1,y-1=2或x-1=-1,y-1=-2或x-1=-2,y-1=-1
解得:x=3,y=2或x=2,y=3或x=0,y=-1或x=-1,y=0