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From: cjh@petsd.UUCP (Chris Henrich)
Newsgroups: net.math
Subject: Re: A number theory problem
Message-ID: <630@petsd.UUCP>
Date: Wed, 28-Aug-85 18:10:11 EDT
Article-I.D.: petsd.630
Posted: Wed Aug 28 18:10:11 1985
Date-Received: Fri, 30-Aug-85 20:18:19 EDT
References: <388@aero.ARPA> <946@oddjob.UUCP> <628@petsd.UUCP> <949@oddjob.UUCP>
Reply-To: cjh@petsd.UUCP (PUT YOUR NAME HERE)
Organization: Perkin-Elmer DSG, Tinton Falls, N.J.
Lines: 28
Summary: 

[]
In article <949@oddjob.UUCP> matt@oddjob.UUCP (Matt Crawford) writes:
>Thanks for the proof outline, Christopher.  I see that the
>hardest part is left out, though -- counting the duplicate
>solutions for U's that are conjugate or related by factors
>of i.  Is the condition something along the line of all
>            _
>the Z's and Z's not being divisible (over the gaussian
>                  _
>integers) by W or W?

Yes.  And that there is "unique factorization" in the Gaussian
integers.  

By the way, the attempt to generalize these ideas to other
quadratic forms was carried out by Gauss, and led to the
modern theory of ideals in rings of algebraic integers.
Part of that theory, called "class field theory", is very
tough stuff.

Regards,
Chris

--
Full-Name:  Christopher J. Henrich
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