1975 IMO Problems/Problem 6

Find all polynomials $P$ , in two variables, with the following properties:

(i) for a positive integer $n$ and all real $t, x, y$ $P(tx, ty) = t^nP(x, y)$ (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) $P(1, 0) = 1.$

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