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every 3 var polymial = equal 2 3 var. polynomials

Source: Polish MO Finals 1980 p4

August 24, 2024
algebrapolynomial

Problem Statement

Show that for every polynomial WW in three variables there exist polynomials UU and VV such that: W(x,y,z)=U(x,y,z)+V(x,y,z),W(x,y,z) = U(x,y,z)+V(x,y,z), U(x,y,z)=U(y,x,z),U(x,y,z) = U(y,x,z), V(x,y,z)=āˆ’V(x,z,y).V(x,y,z) = -V(x,z,y).
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