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polynomials of three variables with rational coefficients

Source: SRMC 2023, P4

December 28, 2023
algebrapolynomialMultivariable

Problem Statement

Let M=Q[x,y,z]\mathcal{M}=\mathbb{Q}[x,y,z] be the set of three-variable polynomials with rational coefficients. Prove that for any non-zero polynomial P∈MP\in \mathcal{M} there exists non-zero polynomials Q,R∈MQ,R\in \mathcal{M} such that R(x2y,y2z,z2x)=P(x,y,z)Q(x,y,z). R(x^2y,y^2z,z^2x) = P(x,y,z)Q(x,y,z).
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