Date: Dec 30, 2012 2:51 PM
Author: quasi
Subject: Re: From Fermat little theorem to Fermat Last Theorem

John Jens wrote:

>I pick a < p ,proved that do not exist a , b , c
>rational numbers with 0<a=<b<c and a<p to satisfy
>a^p+b^p=c^p


No, you never proved the above claim.

You only thought you did.

First you tried to show that the equation

a^p + b^p = c^p

has no solutions in integers a,b,c,p subject to the
conditions 0 < a <= b < c, p > 2, a < p.

For the sake of argument, let's allow that claim.

Then you attempted to extend to positive rationals a,b,c. To do
that, you scale a,b,c down, dividing each by a positive integer
large enough so the new value of a is less than p. Then you
claim a contradiction since you already showed that a < p is
impossible. But you showed that for positive integer values of
a, not for positive rational values of a, so (barring circular
reasoning) you don't have your claimed contradiction.

quasi