Integral Domains: Products of Irreducibles

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I'm suppose to find an integral domain where NOT every element (not a unit) is expressible as a finite product of irreducibles.

I'm not sure where to begin, actually. So perhaps someone can give me a tip, and we can start working our way through this. Thanks..
 
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Thank you anyway, all. Since I have other algebra problems that I need help on, I'm going to include this problem in another thread, joining all the problems.
 
closed...see "ALGEBRA PROBLEMS"
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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