> > Can you tell me where the flaw is, in arriving at
> the statement that Z = Y+X1, where X1 is a factor of
> X^N?

> > Regards

> > Phil

> Hi Phil,

> I will speak to the flaws in your presentation.
>  Since this thread
> doesn't give a clue as to what you said and where you
> said it, I had
> to hunt before I could find it.  It would be easier
> for the group and
> help you get replies if you would give a link or at
> least a clue as to
> where to find your work.  Of course the
> responsibility was really
> master1729's.

> Anyway, let's start with what you said about the case
> N = 2.  Here is
> what you said:

> Start Quote
> What happens when N=2?

> When N=2, Z^2 – Y^2 = X^2 and this can be broken down
> into (Z-Y)(Z+Y)
> so that X^2 is the product of (Z-Y) or X1, and (Z+Y)
> or X2. Solutions
> can be found for any situation where X1 is an odd
> power of X and X2 is
> a higher odd power of X multiplied by 1 or another
> number raised to
> the same power. Therefore it is clear that there must
> be an infinite
> number of solutions for N=2.
> End Quote

> Really?  Why is that clear?  You are claiming that it
> is clear (=
> obvious) that we can always find Y and Z such that
> Y-Z is an odd power
> of X and Y+Z ... as you said above.  First of all,
> this is simply
> wrong for then their product could be larger than X^2
> and larger is
> not equal to.  However, they only need to be an odd
> power of anything
> and so on as you say without reference to the X.  But
> you need to
> prove that you can always find that and it is really
> far from obvious
> to me.  I only know that this equation, X^2 + Y^2 =
> Z^2 has infinitely
> many solution because I have read an actual proof
> that doesn't simply
> leave out the most important step.

> Now to your absurd claim about N larger than 2.  It
> is hard for me to
> point to a specific error, because it is completely
> incoherent.  Write
> it coherently and I will be glad to review and tell
> you where your
> errors are.

> Notes on Style:
> 1) You spend a long time justifying the obvious fact
> that if Z^3 - Y^3
> = X^3 then X^3 is divisible by Z - Y.  I say it is
> obvious because I
> remember the factorization

> Z^2 - X^3 = (Z - Y)*(Z^2 + ZY + Y^2)

> which I learned in a Junior High School algebra
> course and still
> remember.  You never actually present the analogue
> for N larger 3, but
> the same general idea works for any N.

> 2) You spend a lot of time making the point that X^N
> + Y^N = Z^3 is
> logically equivalent to
> Z^N - Y^N = X^N.  Yes, you can subtract the same
> things from both
> sides of an equation and the equality still holds.
>   You can add the
> same thing too, so the resulting equation is
> logicallyl equivalent.
> Duh.  Just state things like this.  They need no
> justification.

> 3)  In you proof section, you say
> Start Quote
> There is evidence for a relationship between two
> numbers where one is
> subtracted from the other when they have the same
> power.
> End Quote

> There is rarely a place for saying that there is
> evidence for
> something in a proof as part of the proof.  Your
> style will be
> improved if you just stick to the facts.

> 4) Similarly to point 3), your proof section is very
> chatty, and that,
> combined with the fact that a lot of the chat does
> not make a lot of
> sense, makes the part of your "proof" that do make
> sense harder to
> follow, probably for you as well as for the reader.

> I appreciate that you have a love of mathematics, but
> please to try to
> learn some before you attempt something as grand as
> Fermat's Last
> Theorem, or any thing much else for that matter.

> Regards,
> Achava