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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