Assume that the number field K contains a primitive n'th root of unity $\displaystyle u$.
Let $\displaystyle a$ in the integral ring of K and let I be an prime ideal of the integral ring of K such that $\displaystyle na$ is not in I.
Let L=K($\displaystyle a^{1/n}$).
Show that $\displaystyle x^{n}-a$ is separable modulo I.


Thank you!!!