IMO 1975 Problem 6

Determine the polynomials P of two variables so that:

a.) for any real numbers $t,x,y$ we have $P(tx,ty) = t^n P(x,y)$ where $n$ is a positive integer, the same for all $t,x,y;$

b.) for any real numbers $a,b,c$ we have $P(a + b,c) + P(b + c,a) + P(c + a,b) = 0;$

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