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September 10th, 2012, 04:25 AM  #1 
Newbie Joined: Sep 2012 Posts: 2 Thanks: 0  Unique factorization domain
Hello!  Exercise: Show that the equation has integral solutions. Deduce that is not a unique factorization domain.  It over a year ago that I had my Algebra lecture, and so I forgot a lot of it.... Also I never had ringtheory very detailed. So I hope someone can tell me some hints how to show that something is (or in this case isn't) an unique factorization domain! I looked up the definition, but as I never really worked with it, I don't know how to start... The Integer solution to the equation are and . Thanks and all the best, Loko 
September 10th, 2012, 05:12 AM  #2 
Newbie Joined: Sep 2012 Posts: 2 Thanks: 0  Re: Unique factorization domain
I figured a little more out So I have with this equation that and thus if and are irreducible, the representation of 125 is not unique... right? If it is right, I would just need help how I could shor the elements to be irreducible. Thanks and best, Loko 

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domain, factorization, unique 
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