```Date: Dec 1, 2012 12:20 AM
Author: vrut25@gmail.com
Subject: Re: From Fermat little theorem to Fermat Last Theorem

On Tuesday, November 27, 2012 10:49:45 PM UTC-8, John Jens wrote:> On Tuesday, November 27, 2012 9:58:32 PM UTC+2, quasi wrote:> > > John Jens wrote:> > > > > > >quasi wrote:> > > > > > >>John Jens wrote: > > > > > > >> > > > > > > >>>http://primemath.wordpress.com/ > > > > > > >> > > > > > > >>Copying part of the text from the link above (enough to > > > > > > >>expose the error in Jens' reasoning) ...> > > > > > >> > > > > > > >>>Fermat?s little theorem states that if p is a prime number, > > > > > > >>>then for any integer a, the number a^p is an integer multiple > > > > > > >>>of p.	> > > > > > >>> > > > > > > >>>   a^p = a(mod p) > > > > > > >> > > > > > > >> Yes, but note that a^p = a (mod p) does not imply 0 <= a < p.> > > > > > >>> > > > > > >>>Assume that a,b,c naturals and p prime and > > > > > > >>> > > > > > > >>>> > > > > > >>> > > > > > > >>>   0 < a <= b < c < p> > > > > > >>>> > > > > > >>> > > > > > > >>> ... > > > > > > >>>> > > > > > >>>So we can?t find naturals 0 < a <= b < c < p with p prime to > > > > > > >>>satisfy a^p + b^p = c^p. > > > > > > >> > > > > > > >> Sure, but that doesn't even come close to proving Fermat's > > > > > > >> Last Theorem. All you've proved is the trivial result that if > > > > > > >> a,b,c are positive integers with p prime such that > > > > > > >> a^p + b^p = c^p then c >= p.> > > > > > >> > > > > > >"Assume that a , b , c naturals and p prime and 0<a=b<c<p"> > > > > > > > > > > > Yes, you can assume anything you want, but then any conclusion > > > > > > is conditional on that assumption.> > > > > > > > > > > > Without loss of generality, you can assume> > > > > > > > > > > >    0 < a <= b < c> > > > > > > > > > > > but how do you justify the inequality c < p?> > > > > > > > > > > > Of course you can take 2 cases:> > > > > > > > > > > >    (1) c < p> > > > > > > > > > > >    (2) C >= p> > > > > > > > > > > > The case you analyzed is the case c < p (the trivial case),> > > > > > and you never even considered the other case. Thus, you > > > > > > did not actually prove Fermat's Last Theorem.> > > > > > > > > > > > quasi> > If a > c and/or b > c it's obvious that a^p + b^p > c^p.> > We ca choose z ,y ,z > p , x <= y < z and using modulus properties a ,b ,c,  a <= b < c ,a < p that x = a + mp ,y = b + np, z = c + qp with m, n ,q naturals > >   (a + mp)^p?(a + mp)(modp)=a + mp + kp=a + p(m+k)...You don't know when to stop, do you?
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