Re: Bring Math Arguments against this FERMAT LAST THEOREM PROOF

quasi wrote:
> On Mon, 29 Aug 2005 17:41:31 EDT, george ghiata
> <george_ghiata@xxxxxxxxxxx> wrote:
>
> >Hello,
> >In the case X*Y*Z divisible by 3 I need only to consider
> >the case Z divisible by 3
> >because X,Y ,Z are INTEGERS(NOT natural numbers)
> >george
>
> Ok, fine -- and while you never said that in your proof (many readers
> would have assumed you were talking about positive integers), by
> allowing X,Y,Z to be integers, not necessarily positive, that does
> deal with the objection.
>
> Even though you are writing the equation in the form X^3+Y^3=Z^3 which
> is not fully symmetic, the fact that the variables X,Y,Z are not
> required to be positive allows the names and signs to be adjusted so
> that if any one of X,Y,Z is a multiple of 3, then we can assume it's
> Z.
>
> So, with that understanding, the 2 cases you originally specified are
> OK. Just make sure that later you don't try to assert an inequality
> which implicitly assumes a positivity that we're abandoning right
> here.
>
> So you have these 2 cases:
>
> case 1: X,Y,Z are not multiples of 3 (equivalently, X*Y*Z is not a
> multiple of 3).
>
> case 2: Z is a multiple of 3 (but X,Y are not multiples of 3).
>
> Ok, Matt, pass the ball back to you. Does that satisfy your
> objections?
>

My understanding of George's response to my comments is that the proof
we are looking at right now deals with your case 1 (X*Y*Z not divisible
by 3) and not, as George originally stated, Z not divisible by 3.

If this understanding is correct then the assumption that X is not
divisible by 3, which I queried, is justified. Also, the consideration
of Y divisible by 3 is unnecessary, as George has I believe
acknowledged. Therefore I believe we are OK so far, as far as these
points are concerned.

I also understand that George claims a second, similar proof that
covers, in some fashion or other, X*Y*Z divisible by 3. To avoid
unnecessary confusion I propose that we leave this second case for now.
Once the status of the "X*Y*Z not divisible by 3" proof has been
established, we can, if necessary, return to the second case.

.

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