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September 10th, 2012, 05:25 AM   #1
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Unique factorization domain

Hello!

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Exercise:
Show that the equation has integral solutions. Deduce that is not a
unique factorization domain.
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It over a year ago that I had my Algebra lecture, and so I forgot a lot of it....
Also I never had ring-theory 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
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September 10th, 2012, 06:12 AM   #2
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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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