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 $$ f(a − b) + f(b − c) + f(c − a) = 2f(a + b + c). $$
| Attributes | Олімпіадна |
|---|---|
| Source | International Mathematical Olympiad |
| Year | 2004 |
| Number | 2 |
| Difficulty | 10.0 |
| Themes | Геометрія |