From: dredmond@math.siu.edu (Don Redmond)
Subject: Re: A few number theory proofs
Date: Wed, 10 Feb 1999 18:31:36 -0600
Newsgroups: sci.math
Keywords: Citations for some classic Diophantine problems

In article <79s89s$kgq$1@nnrp1.dejanews.com>, allenl@my-dejanews.com wrote:

> Hi.
> 
> I've driven myself nuts looking for these proofs, any help would be very much
> appreciated:
> 
> Fermat's "n=5 and m=3 are the only integral solutions to n^2+2=m^3"
> Euler's "Every prime of the form 6n+1 can be written as a^2+3b^2"
> 
Since I obviously don't know my primes (or how to divide, either) I hesitate
to answer, but think you can find these, or at least the methods to do
them in a number theory test by Allenby and (Redfern?). Unfortunately I
can't even remember the title other than to obviously say that number
theory is
in it somewhere.
>
> And of course, the FLT proofs: Dirichlet & Lagrange's for exponent 5,
> Dirichlet's for exponent 14, and Lamé's for exponent 7
> 
Try Edwards' book on Fermat's Last Theorem (or whatever the correct title is;
it's called a genetic intro. alg. no. thy., but I wouldn't trust my
memory.) Or Ribenboim's book "13 Lectures on FLT". The only place I can really
recall seeing Dirichlet's proofs is in his collected works.

Don
==============================================================================
[For the first, see 99/cubesquare. For the 
 second, see  99/qform --djr]