Determine the polynomials P of two variables so that:
a.) for any real numbers
![t,x,y](/media/m/e/3/7/e372c175642b96cc37d455cd80c35b23.png)
we have
![P(tx,ty) = t^n P(x,y)](/media/m/f/a/9/fa98ffbd937dca9817b50c3500b5c9c1.png)
where
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
is a positive integer, the same for all
b.) for any real numbers
![a,b,c](/media/m/3/6/4/36454fdb50fc50f021324b33a6b513e3.png)
we have
c.)
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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.) $P(1,0) =1.$