\(P\cdot x^2y=x^3y^2-x^3y-x^2y^2+x^2y\)
=>\(P=\dfrac{x^3y^2-x^3y-x^2y^2+x^2y}{x^2y}\)
\(\Leftrightarrow P=xy-x-y+1=\left(y-1\right)\left(x-1\right)\)
P=2
=>\(\left(x-1\right)\left(y-1\right)=2\)
=>\(\left(x-1;y-1\right)\in\left\{\left(1;2\right);\left(2;1\right);\left(-1;-2\right);\left(-2;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(2;3\right);\left(3;2\right);\left(0;-1\right);\left(-1;0\right)\right\}\)
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