Question

Tìm x;y thuộc N sao cho:

a, xy=x+y

b, xy=p(x+y) với p nguyên tố

Answer 1

a) \(xy=x+y\Rightarrow xy-x-y=0\)

\(\Rightarrow xy-x-y+1=0+1=1\)

\(\Rightarrow x\left(y-1\right)-\left(y-1\right)=1\)

\(\Rightarrow\left(x-1\right)\left(y-1\right)=1\)

\(\Rightarrow x-1;y-1\inƯ\left(1\right)=\left\{-1;1\right\}\)

x-1	-1	1
x	0	2
y-1	-1	1
y	0	2

Vậy (x;y)={(0;0);(2;2)}