1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Irreducible polynomials

  1. Mar 5, 2008 #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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It's a very small problem. Have you tried brute force?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Irreducible polynomials