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f(xy)+f(yz)+f(zx)=f(xy+yz+zx), x+y+z=0

Source: 2022 Thailand October Camp 2.6

February 26, 2022
polynomialalgebra

Problem Statement

Find all polynomials ff with real coefficients such that for all reals x,y,zx, y, z such that x+y+z=0x+y+z =0, the following relation holds: f(xy)+f(yz)+f(zx)=f(xy+yz+zx).f(xy) + f(yz) + f(zx) = f(xy + yz + zx).
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