Find all polynomials with real coefficients such that for all reals such that we have the following relations
%V0
Find all polynomials $f$ with real coefficients such that for all reals $a,b,c$ such that $ab+bc+ca = 0$ we have the following relations
$$f(a-b) + f(b-c) + f(c-a) = 2f(a+b+c).$$
Izvor: Međunarodna matematička olimpijada, shortlist 2004
Školjka 
with real coefficients such that for all reals 
such that 
we have the following relations 