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Irreducable ploynomial in Z5

  1. Aug 21, 2008 #1
    F= x^3 + 2x + 1 irreducable in Z5 (Z subscript 5)

    i have tried EC looking at F(x+1) which doesnt work for me. Cant think of what else to try.

    Help much appreciated. Need to know this for an exam later! ahhh
  2. jcsd
  3. Aug 21, 2008 #2


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    irreducibility of a cubic over a small finite field is trivial because it suffices to show there are no roots.
  4. Aug 21, 2008 #3
    Ok so the only possible roots are 1 2 3 4 or 5 is this correct? Thanks so much for your reply! i have an exam is a few hours with this on it!

    Edit: or is +-1 the only possible roots? Thanks again
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