Fermat's Last Theorem CLARIFICATION
k.p.collins at worldnet.att.net
Thu Jun 6 04:52:49 EST 2002
Kenneth Collins wrote in message
<93zL8.23329$LC3.1751601 at bgtnsc04-news.ops.worldnet.att.net>...
>The Proof of FLT is quite simple.
>"Among Fermat's cherished Latin translations of ancient texts was a book
>called _Arithmetica_, written by the Greek mathematician Diophantus who
>lived in the third century A.D. Around 1627, Fermat wrote in Latin in the
>margin of his Diophantus, next to a problem on breaking down a squared
>number into two squares:
>'On the other hand, it is impossible to separate a cube into two cubes, or
>byquadrate into two biquadrates, or generally any power except a square
>two powers with the same exponent. I have discovered a truly marvelous
>of this, which, however, the margin is not large enough to contain.'"
>[_Fermat's Last Theorem_, by A. D. Aczel, [c] 1996, ISBN0-385-31946-0, p9]
>Fermat's Last Theorem: x^n + y^n = z^n has no whole number solution where n
>is greater than 2." [ibid, pviii.]
>1. when n=2, the equation restates the Pythagorean Theorem, in which z^2
>forms the hypotenuse of a right triangle.
>2. the Pythagoreans verified that, when n>2, the hypotenuse of a right
>triangle is Incommensurable. there exist no unit measures other than 1 and
>2, all the way out to infinity, that can measure the lengths sides of the
>triangle and the length of its hypotenuse.
sorry, 2. is not what i meant to state (i don't even know if it's True :-)
it's the ratio of side to hypotenuse that's incommensurate.
what's important is that this property defines the Fermat equation in an
>3. integers are discrete.
>4. it follows from integer-discreteness and infinitely-rigorous Pythagorean
>incommensurability, that if n=2 works, then no integer >2 can work in the
>Fermat equation. [1 'works' because any number raised to the 1-power is
>the original number, so the equation becomes non-exponent-ed [x + y = z],
>which isn't the equation of FLT.]
>i believe that this simple Proof is a good candidate for what was in
>Fermat's mind when he wrote the problem in the margin of the book he was
>i'd stated it [using other words; "a square is a square..."]] before
>the Author's article. After reading the article, i wrote a program that did
>a numerical analysis. the program verified that all integers >2 behave
>asymptotically re. the Fermat equation. this asymptotic stuff reiterates
...with specific respect to the Fermat equation.
a Square is an infinitely-precise entity.
when n=2, the Fermat equation describes a Square.
if it's infinitely-precise, and the integers are discrete, then it cannot be
reproduced for n>2.
it is. they are.
why all this 'hubbub?
"because it's there."
>other matter: if folks want to get a handle on all the data that's been
>'slipping-through' [FBI, CIA, NSA], its meaning undetected, and
>unintegrated. i'll be happy to show [those folks] how to build a system
>can do the Integration and present its integrated-meaning in a way that's
>accessible in 'real-time' [with respect to putting the info in].
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