IMO 2019 Shortlist A6
A polynomial Ppx,y,zq in three variables with real coefficients satisfies the identities Ppx,y,zq “ Ppx,y,xy ´ zq “ Ppx,zx ...
Category: Algebra
Problem
A polynomial Ppx,y,zq in three variables with real coefficients satisfies the identities
Ppx,y,zq “ Ppx,y,xy ´ zq “ Ppx,zx ´ y,zq “ Ppyz ´ x,y,zq.
Prove that there exists a polynomial Fptq in one variable such that
Ppx,y,zq “ Fpx2
y2 z2
´ xyzq.
(Russia)