There is a theorem about one variable polynomials which tells a polynomial of degree $n$ has at most $n$ roots which helps us to recognize polynomials that are identically zero. At this problem we had:
$A(a,b,c)\implies cQ(ab,c^2+1)+aQ(bc,a^2+1)+bQ(ca,b^2+1)=0$
for non-zero $a,b,c$ and we concluded it for all real numbers. More generally when can we do that in multivariable polynomials?
