Recent content by stoolie77

So CRGreathouse, my assumption above fails then? And then you're saying that \epsilon and \gamma are both 1, and then you say that any factorization is of this form, not just this example, right?

Thank you CR Greathouse! I'm still confused on how to relate this to the variables though and what you have written above. I think this is what you have written above: 32=2^5=(1-i)^5 (1+i)^5 So when I try to relate that to something of the form 32=\alpha\beta where \alpha=\epsilon...

Hello Robert, could you expand on this? I don't see how it directly relates to my example of 32 considering you used values that net a 2. Could you use some of the variables as well (some sort of General notation)? I'm just lost in connecting what you're saying to what I'm trying to figure out...

Hello everybody. I found this example online and I was looking for some clarification. Assume 32 = \alpha\beta for \alpha,\beta relatively prime quadratic integers in \mathbb{Q}[i]. It can be shown that \alpha = \epsilon \gamma^2 for some unit \epsilon and some quadratic \gamma in...

Hello everybody. I had been reading up on Unique Factorization again and I came across an interesting question. Can someone prove unique factorization for the set of polynomials in x, with integer coefficients? From what I understand, the analogous Euclidean algorithm works for such...

interesting thread. I've tried my best to follow along and i believe that this is all you need to do. hochs should confirm it first though as he's beek working with you this whole time.

Mathhelpforum.com is quite good.