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Galois Theory - irreducibility over Q

  1. Oct 17, 2011 #1
    1. The problem statement, all variables and given/known data

    If a>1 is a product of distinct primes, show that xn-a is irreducible over Q for all n ≥ 2.

    2. Relevant equations



    3. The attempt at a solution

    I am not really sure how to start this problem. Can anyone point me in the right direction?

    I know tests for irreducibility for example Eisensteins Criterion or reduction modulo p but I don't think that these are helpful here?

    Thanks for any help.
     
  2. jcsd
  3. Oct 17, 2011 #2

    I like Serena

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    Hi Kate2010! :smile:

    How about the rational root theorem?
     
  4. Oct 17, 2011 #3

    Dick

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    That would only tell you it doesn't have any linear factors. I'm a little confused why Kate2010 thinks Eisenstein's criterion isn't applicable.
     
  5. Oct 17, 2011 #4

    I like Serena

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    Right.
    Just looked up Eisenstein's criterion.
    Looks like a good one. :)
     
  6. Oct 18, 2011 #5
    Thanks guys - I was trying to make things more complicated than they were.
     
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