Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: From Fermat little theorem to Fermat Last Theorem
Replies: 62   Last Post: Mar 14, 2013 9:59 PM

 Messages: [ Previous | Next ]
 Pubkeybreaker Posts: 1,683 Registered: 2/12/07
Re: From Fermat little theorem to Fermat Last Theorem
Posted: Nov 29, 2012 12:15 PM

On Wednesday, November 28, 2012 3:07:56 PM UTC-5, quasi wrote:
> John Jens wrote: >Corrections was made. > >It's sufficient that only a < p. But you never _proved_ the inequality a < p, so you don't get to use it. Moreover, the equation a^p + b^p = c^p with the restrictions a,b,c positive integers p prime does not imply min(a,b) < p. To see this, just use p = 2 with a,b,c = 3,4,5. You tried to argue that you can't have p=2 since the inequality min(a,b) < p would then force min(a,b) = 1, leading to an easy contradiction. But you can't use the inequality min(a,b) < p without proving it, and the example p = 2 with a,b,c = 3,4,5 makes it clear that you can't prove it. quasi

A global remark:

It was demonstrated a number of years ago that FLT can not be proved
by modular considerations such as the one presented by the O.P.

The reason is as follows: The Hasse-Minkowski theorem that allows diophantine
analysis over a local field (such as Z/pZ) to be lifted to a global field
(such as Q) is blocked for FLT by the fact that SHA (The Tate-Sharfarevic
group) is non-trivial except in the case n = 4 (which is also why descent
argument works for n = 4). It is similar to the Brauer group obstruction
that prevents Abelian Varieties over local fields from being lifted to Q.

(I realize that the level of the discussion has been raised to the research
level of algebraic geometry; which, of course, is what Wiles used to
prove the thoerem)

Date Subject Author
11/27/12 John Jens
11/27/12 quasi
11/27/12 John Jens
11/27/12 quasi
11/27/12 Pubkeybreaker
11/28/12 John Jens
11/28/12 quasi
11/28/12 John Jens
11/28/12 Frederick Williams
11/28/12 John Jens
11/29/12 David Bernier
11/29/12 Michael Stemper
11/28/12 Ki Song
11/28/12 John Jens
11/28/12 gus gassmann
11/28/12 John Jens
11/28/12 Ki Song
11/28/12 quasi
11/29/12 Pubkeybreaker
11/28/12 John Jens
11/28/12 quasi
12/1/12 vrut25@gmail.com
12/2/12 John Jens
12/2/12 quasi
12/2/12 quasi
12/29/12 John Jens
12/29/12 J. Antonio Perez M.
12/30/12 John Jens
1/5/13 John Jens
1/5/13 J. Antonio Perez M.
1/5/13 John Jens
1/6/13 Michael Klemm
1/6/13 John Jens
1/6/13 Michael Klemm
1/7/13 John Jens
1/7/13 Michael Klemm
1/7/13 Pubkeybreaker
1/7/13 John Jens
1/7/13 Bart Goddard
1/7/13 Michael Klemm
1/7/13 John Jens
1/7/13 Michael Klemm
1/7/13 John Jens
1/7/13 Michael Klemm
3/7/13 Brian Q. Hutchings
3/14/13 Brian Q. Hutchings
12/29/12 quasi
12/30/12 John Jens
12/30/12 quasi
12/30/12 John Jens
12/30/12 quasi
12/31/12 John Jens
12/31/12 quasi
12/31/12 quasi
1/2/13 Brian Q. Hutchings
1/4/13 John Jens
1/4/13 quasi
1/4/13 John Jens
12/30/12 Pubkeybreaker
12/30/12 John Jens
12/30/12 Pubkeybreaker
11/27/12 wheretogo