are you going completely nuts and just throwing everything, including the kitchen sink, into the mix?

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- 02-10-2017, 06:06 PM #1

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## Fermat's Theorem, Relativity, Quantum Field Theory

**Proof of Fermat's Theorem**

I will be tracking (most) updates to this proof here

Updates to Proof of Fermat's Last Theorem

(The is an "on the fly" update; make sure your cache is empty to get the latest version; even then, there may be some lag.)

**If Fermat's expression were true (), , , and would be a Pythagorean Triple. They are not a Pythagorean Triple by the Binomial Theorem, where rem(a,b,n) > 0.**

**Therefore,****, for a,b,c,n positive integers, n>2**

See post #81 for diagram.

QED

The dates in my signature reflect the most recent updates - and they are still a work in progress.

**To the reader: Please read my Ignore List before continuing.**

This is the link to my proof of Fermat's Theorem. Some in this thread bray "Nonsense" without context like jackasses - only Grapes seems to read documents and critique in context (occasionally), alerting me to possible algebraic errors, which are much appreciated for what they are (I'm writing a lot of tex and have no proofreader). However, as of this date (2/24/2017) he has yet to learn that triangles are expressed in two dimensions, rather than one, and therefore the significance of the dot product in Pythagorean triangles, not to mention the more general cases of circles, squares, and volumes.

Neither Neverfly nor The Naked Emperor have any idea WTF I am talking about as will be clear from their posts ....

The context of the proof is that for two generalized variables, two dimensions are required for mathematical (i.e., arithmetical) operations on real numbers as well as integers. This is because the dimensions have to be related by a common metric (i.e., must touch, cannot be parallel in two dimensions), so there is a common connection (the "zero" point, which defines the origin of each dimension as the midpoint of all possible lengths for that dimension). Thus, two dimensions must have a common origin in order to compare metrics.

This is true for real numbers, as well as integers, which is why the Binomial Theorem is applicable - Pythagorean Triplets begin with orthogonal dimensions, and the case for powers is expanded via the Binomial Expansion.

If there is no such connection, it can be removed by "imaginary" (no pun intended); i.e. complex numbers, which is an operation fundamental to the Pauli characterization of "spin" via the and matrices which treats number lines on either side of the origin as independent (1,-1), expanded by Dirac to the complete description of the circle (1,-1,1,-1).

The Relativistic Unit Circle shows that the first integer for positive definite integers is created as when an arbitrary metric is applied via the so-called "time dilation" equation.

Quantum Field Theory then applies the result to two dimensions (1,1) where for positive definite quantities equally and oppositely directed in terms of the null vector, like the analysis above, where the interaction in terms of n and h can be identified with 2ab from the Binomial Expansion for n=2.

The derivative then becomes a function of first dividing out the successive interactions given by (a+b), and then taking the limit as b ->0, so that multiplied by the null vector. (if a=0, there is no integer to begin with). When this is accomplished, the constant a can be identified with the slope of a straight line in the coordinate relation y = Ax, a = A, where the derivatives can then be identified with the Jacobian of the metric tensor in GTR.

The constant can be identified as the "mass" of a particular photon relative to the "zero point" energy at which the photon has no perceived mass (e.g., the parking lot on earth, unless you get a sunburn). The "c" is identified as a specific value (t=1) from the "measured" displacement current from Maxwell's equation, via the force constants from Ampere's and Coulomb's laws.

The process of setting h and n equal to zero in the QFT characterization removes interactions from the theory to the two dimensional characterization of Dirac for two photons (photon -equivalent particles by deBroglie), and finally two a single photon by setting so the energy of the single photon is given by where c has a different value for each photon depending on its relation to the zero point energy.

Probabilistically, that energy is usually given by a Gaussian spread around some reference black-body temperature in the parking lot. The context can be expanded to the solar system, the galaxy, and beyond if one uses one's fertile imagination. May the Force be with you.. (it ain't with me, as far as I know...Last edited by BuleriaChk; 03-03-2017 at 03:11 PM.

_______________________________________

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/28/2017 07:40 AM PST**

Proof of Fermat's Last Theorem Updates**03/19/2017 8:23 PM PST**

**Ignore List -The Peanut Gallery.**

- 02-11-2017, 11:21 AM #2

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## Re: Fermat's Theorem, Relativity, Quantum Field Theory

are you going completely nuts and just throwing everything, including the kitchen sink, into the mix?

- 02-13-2017, 05:36 PM #3

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## Re: Fermat's Theorem, Relativity, Quantum Field Theory

I have revised the OP to reflect a corrected error, and its relevance to STR, GTR, QFT, and Foundations of Mathematics.

_______________________________________

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/28/2017 07:40 AM PST**

Proof of Fermat's Last Theorem Updates**03/19/2017 8:23 PM PST**

**Ignore List -The Peanut Gallery.**

- 02-14-2017, 06:33 AM #4

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## Re: Fermat's Theorem, Relativity, Quantum Field Theory

Still same old errors of trying to use binomial.

- 02-14-2017, 10:24 AM #5
## Re: Fermat's Theorem, Relativity, Quantum Field Theory

???

Your "proof" of Fermat's Last Theorem is a mess.

Has nothing to do with the Axiom of Choice.

Then dividing each side by results in .

If then so that .

If then so that .

If neither nor , then AND , so that neither can be an integer ( cannot be a lowest common denominator; i.e. unless the integers form a Pythagorean Triple).

But, of course a/c and b/c are not integers, because they're less than 1

Therefore

which is the case for the Binomial Expansion for , where , .

Note that if is not an integer,

then cannot be an integer so cannot be an integer; neither can kc for any integer k, so cannot be an integer.

The case for can easily be extended for , since , where , and only disappears if or , as in the one-dimensional case.

Then QED (i.e., Fermat's Theorem is valid).

- 02-14-2017, 12:42 PM #6

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## Re: Fermat's Theorem, Relativity, Quantum Field Theory

I have revised my pdf Fermat's Last Theorem in the OP to include the fact that the scalar coefficients of vectors in the space (a,b) commute even without the real metric comparison, which means there is the interaction product 2ab even in the case of Pythagorean triplets, which makes them completely consistent with the Binomial Expansion for the case n=2 and the results of the Dirac formulation in Quantum Field Theory.

My signature pdf has also been updated to include this analysis with reference, but I have removed most of the material relating to Fermat there (except for the link), so it is more focused on the relation of the Binomial Expansion to Quantum Field Theory and GTR...

In all cases, refer to the pdf's from the OP, since they are the latest update of my work. There is not much point in making the effort to write tex redundantly here. If you think you have a real criticism, pm me.

(I do make algebraic mistakes on occasion, since it is difficult for me to keep the overall conceptual ideas clear.)Last edited by BuleriaChk; 02-14-2017 at 07:16 PM.

_______________________________________

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/28/2017 07:40 AM PST**

Proof of Fermat's Last Theorem Updates**03/19/2017 8:23 PM PST**

**Ignore List -The Peanut Gallery.**

- 02-14-2017, 03:23 PM #7
## Re: Fermat's Theorem, Relativity, Quantum Field Theory

- 02-14-2017, 06:52 PM #8

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## Re: Fermat's Theorem, Relativity, Quantum Field Theory

Tried the algebra again. I think it is correct now, but I get nightmares about this stuff. I believe the analysis is correct. I'll continue to revisit it.

The analysis provides an alternative definition to the derivative (that John Gabriel was attempting) in terms of linear system theory.

(That's why Dirac and Pauli got the big bucks....

The point is that the basis of the relativistic unit circle's energy in one dimension is , which is the first integer with a single basis in one dimension (the basis interacts with itself). For two integers (bases), the energy of the circle is if there is no interaction (so just raw "counting" applies subjectively - 2ab=0). For higher dimensions (integers) the diagram is no longer a circle, but the interactions are handled in terms of quantum field theory, where the initial state is invariant for the interpretations.

However, if there is a common origin, then Pauli and Dirac introduce parity as independent variables, which give the (equivalent) resultant interaction of for a = b = 1.

The analysis therefore doesn't involve c until the very end, since the interaction is created by the (hypothetical) linearity of (a,b) if there is a common origin (the vectors are not "affine" -i.e., parallel but different in one dimension). That was the source of Einstein's Parallel transport" to try to introduce gravity (or god) as an additional force to that of electromagnetism interpreted as c (the foundation of observation).Last edited by BuleriaChk; 02-14-2017 at 07:43 PM.

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/28/2017 07:40 AM PST**

Proof of Fermat's Last Theorem Updates**03/19/2017 8:23 PM PST**

**Ignore List -The Peanut Gallery.**

- 02-14-2017, 11:17 PM #9

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## Re: Fermat's Theorem, Relativity, Quantum Field Theory

Malaria, do you even know what the axiom of choice is?

- 02-15-2017, 01:00 AM #10

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## Re: Fermat's Theorem, Relativity, Quantum Field Theory

Once more into the breach - yet another shot at the algebra in the PDF. I really think it is ok now. (the Proof is still valid)

As an exercise, set a = b = 1 in the Expansion

for a model of the basis set (1,1) in two dimensions...Last edited by BuleriaChk; 02-15-2017 at 10:23 AM.

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/28/2017 07:40 AM PST**

Proof of Fermat's Last Theorem Updates**03/19/2017 8:23 PM PST**

**Ignore List -The Peanut Gallery.**

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