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Topic: Three different proofs of Fermat's Last Theorem(1) Generalized FLT
(2) Geometry using notched cubes (3) Duality of Numbers to Angles

Replies: 5   Last Post: Oct 4, 2017 12:38 AM

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 plutonium.archimedes@gmail.com Posts: 18,572 Registered: 3/31/08
demonstration of how this proof works Re: what a beauty Re: the sheer
dazzling beauty of this Third proof of FLT

Posted: Oct 3, 2017 7:43 PM

On Tuesday, October 3, 2017 at 4:21:17 AM UTC-5, Archimedes Plutonium wrote:
> Yes, what a beautiful proof that was, the third proof of FLT, simply stated, no solution exists for exp3 or higher, because any solution there would cascade down to a x,y,1 solution such as 3,4,5 is .6, .8, 1 and so all possible solutions are covered only by exp2. Otherwise you would have A^2 = A^3 or A to the whatever exponent.
>
> Now that proof does the Array honor, because the proof statement is one paragraph and equal to or smaller than the Theorem statement.
>
>

Alright, so, let us try a test run sample of the meaning of this proof of FLT. We have a good sample in exp3 of 9^3 + 10^3 = 12^3 + 1 where it misses by 1.

So let us ignore the 1 and then go ahead with pretending that it is a solution.

So we have .75^3 + .833..^3 = 1^3
that is .4218... + .5787... =1

Now, how does the proof work?

Well, it says that if any solution, any at all exists is exp3 or higher, any solution.

By arithmetic of law of exponents, that solution can be reduced to a form of x,y,1 where x and y are between 0 and 1 such as our .42... and .57...

So, what is wrong with that solution? What is impossible about it?

It is impossible because we already have that solution in exp2 of Pythagorean theorem

For if we take the square root of .42... and .57... we have .649 and .76 and 1 and converting that in exp2 to be 649, 760, 1000 (close, but of course off by a little bit).

So, the trouble with ever having a solution in exponents higher than 2, is that there already exists a solution in 2 and thus math would be having a A^2 = A^3 and that only occurs when A= 0 or 1.

AP

On Tuesday, October 3, 2017 at 4:21:17 AM UTC-5, Archimedes Plutonium wrote:
> Yes, what a beautiful proof that was, the third proof of FLT, simply stated, no solution exists for exp3 or higher, because any solution there would cascade down to a x,y,1 solution such as 3,4,5 is .6, .8, 1 and so all possible solutions are covered only by exp2. Otherwise you would have A^2 = A^3 or A to the whatever exponent.
>
> Now that proof does the Array honor, because the proof statement is one paragraph and equal to or smaller than the Theorem statement.
>
> AP