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.

5) The nonsensical philosphical ramblings in your introduction mostly
serve to drive away mathematicians who immediately pick up your vast
ignorance of our subject and who do not have the patience to read what
is already clear will do what you say it will do.

That is enough for now.  I only read the thing to try to give you some
pointers as to what was specifically wrong, but it was hard to find
much that was coherent enough to comment on.

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.