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Homework Help: Prove 29 is not irreducible in Z

  1. Apr 20, 2010 #1
    Prove 29 is not irreducible in Z

    Don't I just have to show here that 29 is a product of 2 elemets in Z?

    So

    29 = (a+bi)(a-bi) where a=5 b=2

    That can't just be it though?

    Thanks
     
  2. jcsd
  3. Apr 20, 2010 #2
    Re: Prove 29 is not irreducible in Z

    Why wouldn't it be it?

    Goal: Show that 29 can be factored over the Gaussian integers.
    Proof (by explicit example): (5 - 2i)(5 + 2i) = 25 - 10i + 10i - 2i^2 = 25 + 4 = 29. QED
     
  4. Apr 20, 2010 #3

    Hurkyl

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    Re: Prove 29 is not irreducible in Z

    Sure it is, depending on how obvious you consider it to be that 5+2i and 5-2i are non-units.
     
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