Search All of the Math Forum:

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

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

 Messages: [ Previous | Next ]
 John Jens Posts: 24 Registered: 11/27/12
Re: From Fermat little theorem to Fermat Last Theorem
Posted: Jan 7, 2013 1:22 AM

On Sunday, January 6, 2013 9:05:08 PM UTC+2, M_Klemm wrote:
> You should give a reason why you assume a < p.
>
> For p = 2 you have 3^2 + 4^2 = 5^2, and then by little Fermat 3 + 4
>
> congruent 5 (mod 2)
>
> but not 3 < 2.
>
>
>
> Regards
>
> Michael
>
>
>
> wrote in message
>
>

> > On Sunday, January 6, 2013 10:56:35 AM UTC+2, M_Klemm wrote:
>
> >> Hello,
>
> >>
>
> >>
>
> >>
>
> >> consider the case p =3, proved by Euler. Then you see that the assumption
>
> >> a
>
> >>
>
> >> < p in line 4 is not at all justified.
>
> >>
>
> >> Regards
>
> >> Michael
>
> >
>
> > I'm sorry but I don't understand what are you trying to say.

The reason is to prove FLT .
Let's split in three steps :
Step 1--> prove a^p + b^p != c^p with a < p ,a,b,c, naturals
Step 2--> extend to rationals , still a < p
Step 3--> pick A >= p, assume A^p + b^p = c^p and scaling down to A/k < p ,k rational -->contradiction to step 2

If a + b ? c>0 because 0<a?b<c implies b ? c < 0 ,
0 ? a + b ? c < a < p
then a + b ? c ? 1 and because a + b ? c < a implies a ? 2 and because a < p implies p > 2

Still a + b ? c>0 ,a + b - c must be at least 1 and with p=2 we can't find natural a between a + b - c and
p there's no Step 1 for p = 2

(If a + b ? c ? 0 we have a + b ? c

(a+b)^p?c^p and using binomial theorem

a^p+b^p<(a+b)^p=a^p+?+b^p?c^p)

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