Re: Fermat

From: Arturo Magidin (magidin_at_math.berkeley.edu)
Date: 11/23/04 

Date: Tue, 23 Nov 2004 20:32:28 +0000 (UTC)

In article <41a39db2$1_2@Usenet.com>,
ben ito <benito20044@yahoo-dot-com.no-spam.invalid> wrote:

  Probably wasting my time, but...

>=================================
>The equations Fermat is using to prove n=4 are derived from the
>integer solution equation of n=2. Fermat is assuming that those
>equation represent all integers which they do not. If Fermat's n=4
>were valid then why doesn't he use his proof to prove n>2 or n=8.
>====================================

The proof for n=4 IMPLIES the proof for n=8. Because, if

x^8 + y^8 = z^8

holds, then

(x^2)^4 + (y^2)^4 = (z^2)^4

holds; thus, knowing that no solutions exist for n=4 (other than the
trivial ones) automatically implies that no solutions exist for n=8
(or for any multiple of 4, in fact) other than the trivial ones.

For that reason, as well, proving FLT is normally restricted to
proving the case n=4 and the case n=p an odd prime. Because, if you
know those, you can deduce every other exponent n>2. 

-- 
======================================================================
"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu
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