Rationalizing fractions over finite fields

  • #1

Homework Statement


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!


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Not sure what is the command for latex but I meant 1/(1 + w^k).
 
  • #3
SteamKing
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Isn't (1 + w^k) a complex number?
 
  • #4
It isn't. It's in a finite field.
 

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