Prove that there isn't a polynomial with $\text {f(x)}^{13} = {(x-1)}^{143}+(x+1)^{2002}$
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?
Solution 1:
Hint: Consider the coefficients of $x^0,x^1$ on both sides of the equation. This suffices.
Solution 2:
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 $f(x)$?