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Rationalizing fractions over finite fields

  1. Jul 4, 2013 #1
    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. jcsd
  3. Jul 4, 2013 #2
    Not sure what is the command for latex but I meant 1/(1 + w^k).
  4. Jul 4, 2013 #3


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    Isn't (1 + w^k) a complex number?
  5. Jul 5, 2013 #4
    It isn't. It's in a finite field.
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