Y by
Let
be the set of three-variable polynomials with rational coefficients. Prove that for any non-zero polynomial
there exists non-zero polynomials
such that ![\[ R(x^2y,y^2z,z^2x) = P(x,y,z)Q(x,y,z). \]](//latex.artofproblemsolving.com/1/8/a/18a597b189c198ad261fcd88f139e7cc7a2796a2.png)
![$\mathcal{M}=\mathbb{Q}[x,y,z]$](http://latex.artofproblemsolving.com/5/a/c/5ac5be746053d9ceabb9223751de427fa1006bc3.png)


![\[ R(x^2y,y^2z,z^2x) = P(x,y,z)Q(x,y,z). \]](http://latex.artofproblemsolving.com/1/8/a/18a597b189c198ad261fcd88f139e7cc7a2796a2.png)
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