TITLE: Prove that there isn't a polynomial with $\text {f(x)}^{13} = {(x-1)}^{143}+(x+1)^{2002}$
QUESTION [16 upvotes]: Prove that there isn't a polynomial with  $\text {f(x)}^{13} = {(x-1)}^{143}+(x+1)^{2002}$
We can easily find out that  $\text {deg}(f) = 154$ 
Then?

REPLY [6 votes]: This, I think, is a nice problem, and deserves a hint rather than an answer.
See what happens with some values of $x$ which are easy to calculate. What does this tell you about the form of $f(x)$?