I am given 2 pieces of information as below:
1)A polynomial $\displaystyle P(z)=\sum_{n=0}^d a_n z^n$
2) For all $n=0,\dots,d$, $\displaystyle \oint_{|z|=1} \frac{P(z)}{(2z-1)^{n+1}} dz = 0 $
Then I am asked to find what is $P(z)$. Am I supposed to use the residue formula and get the $\mbox{residue}=0$ for all $n=0,\dots,d$?