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Homework Help: Irreducible polynomials

  1. Mar 5, 2008 #1
    (1):
    Find all irreducible polynomials of the form [itex]x^2 + ax +b [/itex], where a,b belong to the field [itex]\mathbb{F}_3[/itex] with 3 elements.
    Show explicitly that [itex]\mathbb{F}_3(x)/(x^2 + x + 2)[/itex] is a field by computing its multiplicative monoid.
    Identify [[itex]\mathbb{F}_3(x)/(x^2 + x + 2)[/itex]]* as an abstract group.

    any suggestions please?
     
  2. jcsd
  3. Mar 5, 2008 #2
    no, but I am currently doing problems that look a lot like this. I would really enjoy seeing this problem solved. =).
     
  4. Mar 5, 2008 #3

    Hurkyl

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    It's a very small problem. Have you tried brute force?
     
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