International Mathematical Olympiad 1975 Problem 6

Find all polynomials $P$ in two variables, with the following properties: (i) for a positive integer $n$ and all real $t, x, y$

$$P(tx, ty) = t^n P(x, y)$$

(that is, $P$ is homogeneous of degree $n$), (ii) for all real $a, b, c$,

$$P(b + c, a) + P(c + a, b) + P(a + b, c) = 0,$$

(iii) $P(1, 0) = 1$.