$a+b=c+d$ , $a^3+b^3=c^3+d^3$ , prove that $a^{2009}+b^{2009}=c^{2009}+d^{2009}$ 
Let $a, b, c, d$ be four numbers such that $a + b = c + d$ and $a^3 + b^3 = c^3 + d^3$. Prove that $a^{2009}+b^{2009}=c^{2009}+d^{2009}$.

I've got $a^2+b^2-ab=c^2+d^2-cd$.
I tried squaring or cubing it repeatedly but I didn't get what I wanted. 
Now how do I proceed? 

Use that we get from $$a+b=c+d$$ so $$a^3+b^3+3ab(a+b)=c^3+d^3+3cd(c+d)$$ and $$x^3+y^3=(x+y)(x^2-xy+y^2)$$
