# Rationalizing fractions over finite fields

1. Jul 4, 2013

### burritoloco

1. The problem statement, all variables and given/known data
Let w be a primitive n-th root of unity in some finite field. Let 0 < k < n. My question is how to rationalize

[\tex]\dfrac{1}{1 + w^k}[\tex].

That is, can we get rid of the denominator somehow? I know what to do in the case of complex numbers but here I'm at a loss. Thanks!

2. Relevant equations

3. The attempt at a solution

2. Jul 4, 2013

### burritoloco

Not sure what is the command for latex but I meant 1/(1 + w^k).

3. Jul 4, 2013

### SteamKing

Staff Emeritus
Isn't (1 + w^k) a complex number?

4. Jul 5, 2013

### burritoloco

It isn't. It's in a finite field.