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!

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

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook