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## Relativity, Fermat's Last theorem, and the Binomial Theorem

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### Relativity, Fermat's Last theorem, and the Binomial Theorem

Hi, all,

I am new here, and still don't know how to make the tex and type the same size, or provide titles to links to URL's to my pdf; I would appreciate help. That said,

I have a proof of Fermat's Last Theorem (unlike Wiles' Theorem) that I'd like to present in this thread.

The Binomial Expansion
${(a + b)^n} = {a^n} + {b^n} + rem(a,b,n)$, where $rem(a,b,n)$ is everything that is not $a^n$ or $b^n$ would almost seem to be a proof by inspection. If it is mapped to a single value, the inspection would make it clear that in the equation

$c^n=a^n+b^n+rem(a,b,n)$, would mean that for Fermat's equation $c^n=a^n+b^n$ to hold, then $rem(a,b,n)=0$, which in turn means that $a=0$ 0r $b=0$ for $c$ to be single valued.

Note that in Fermat's expression there are no products of the type $ab=ba$, so that his expression is actually a metric for a Presburger arithmetic. The integers are based on Peano's axioms which does include multiplication, as does the Binomial Expansion. IMO, this is actually a proof of Gödel's theorem, where an arithmetic system without multiplication is not complete, but if it is complete, then it must include non-integers (real and complex)

However, there are subtleties; In my paper, I show how the Special Theory of Relativity creates the field of positive real numbers, of which the integers are a subset from ct=0. For binomials (The Binomial Expansion also applies to positive real numbers), two relativistic circles are necessary as final states (to "reified" real numbers, valid for the final field by adjusting $c,v,t, and t'$. The two circles are required so that independent (a,b) be established on the positive integer plane; again, emphasizing that Fermat's expression does not include multiplicative products such as ab for independent integers (a,b).

(The relativistic unit circles form the bases for the Dirac gamma zero matrix in QFT).

I have two core papers (both of which are works in progress) dealing with this approach with URL's as well as associated update documents with additional details. I would be very interested in discussing them with an open mind I have written a short summary. I do assume that any responder will be interested in the equations (and interpretations of them), and will be open to reading links to Wiki if I provide them...

(Important; m proof is based on the existence of a binomial; that is, two dimensions each with a field, not just one as the number theorists I am familiar insist on discussing, rejecting Descartes from the start... :) This stuff isn't easy for me or anyone else, and sometimes one has to sit quietly in a dark room and think a bit before responding.

If someone will show me how to create a URL where I can title it instead of using the actual URL, I will proved links to both papers and updates for review and discussion.

Thanks for listening; I look forward to an intelligent discussion. And if I'm wrong (or it has already been done), then it still will move the ball forward for me...
BuleriaChk

Posts: 11
Joined: Sat Mar 11, 2017 7:59 pm

### Re: Relativity, Fermat's Last theorem, and the Binomial Theo

The latex here is rendered via a link to John Forkosh's mimetex. It's a bit basic I'm afraid. Let me try something out.

See http://www.forkosh.com/mimetex.html :

\small {(a + b)^n} = {a^n} + {b^n} + rem(a,b,n)

$\small {(a + b)^n} = {a^n} + {b^n} + rem(a,b,n)$

As for your pdf, it's fairly standard. You can type it directly:

http://www.flamencochuck.com/files/Misc ... dDirty.pdf

Or you can type [urI=http://www.flamencochuck.com/files/Misc/QuickandDirty.pdf]QuickandDirtyPDF[/url] which is displayed like this: QuickandDirtyPDF
JohnDuffield

Posts: 147
Joined: Mon Oct 18, 2010 5:01 pm

### Re: Relativity, Fermat's Last theorem, and the Binomial Theo

Ok, I'll give it at try:

Proof of Fermat's Last Theorem

Ok, that worked, thanks.
BuleriaChk

Posts: 11
Joined: Sat Mar 11, 2017 7:59 pm

### Re: Relativity, Fermat's Last theorem, and the Binomial Theo

Updated FLT Updates, with diagrams showing how the charge-to-mass ratio is represented in STR, and also the relation of rem(a,b,n) to the relativistic unit circle on the integer plane (a,b). Also the STR relation between two independent particles showing the relation of the mixing angles to the relativistic unit circle in Quantum Field Theory for Bosons. (Fermions use both negative and positive charge, but are not relevant to FLT via the Binomial Expansion and the Relativistic unit circle.
BuleriaChk

Posts: 11
Joined: Sat Mar 11, 2017 7:59 pm

### Re: Relativity, Fermat's Last theorem, and the Binomial Theo

These are relatively big documents at 22 and 36 pages Chuck. Do I call you Chuck? I'm into relativity, and I'd like to help you, but I'm pushed for time myself. I'm trying to write something that will be akin to http://www.flamencochuck.com/Relativity.html with a variety of chapters or articles. I can see you have headings light as rest mass and the mass of light but I can't see the content. I get the creation of the universe and a 404 page not found. So I've sent you a 6-page essay on mass. It refers to light and relativity. I can give good feedback on relativity, but not Fermat's last theorem. I've focussed on physics, and that doesn't leave much time for things like an + bn = cn. The Lorentz factor is derived from Pythagoras's theorem because of the wave nature of matter.
JohnDuffield

Posts: 147
Joined: Mon Oct 18, 2010 5:01 pm

### Re: Relativity, Fermat's Last theorem, and the Binomial Theo

I just checked "The creation of the Universe" and it came up fine.
The current articles are in my signature. IMO, think of ct as mass and vt' as charge (one interpretation)
Understanding the Unit circle is primary thing - as abstract initial, perturbing, and final states. Then many independent physical quantities can be modeled using beta and gamma. It is a bit rough, since I am concerned more with getting ideas out, rather than organization...
maybe someday. AFAIK, what I've written is consistent with QFT; it is the connection to Fermat's theorem via the Binomial theorem, with RUC's providing the "final state" basis for independent entities. Right now I'm finalizing my perspective on the Pauli/Dirac matrices, the Lorentz transform, and their relation to the vector potential A and the Lorentz force..
BuleriaChk

Posts: 11
Joined: Sat Mar 11, 2017 7:59 pm

### Re: Relativity, Fermat's Last theorem, and the Binomial Theo

Updated FLT Proof with several new articles (one in color on Astrophysics... :)
BuleriaChk

Posts: 11
Joined: Sat Mar 11, 2017 7:59 pm

### Re: Relativity, Fermat's Last theorem, and the Binomial Theo

Updated Relativity document (completely re-written) to include the derivation of the Binomial Expansion from STR by including spin, thus nailiing the proof of Fermat's Theorem, since it applies not only to integers but to real positive numbers, all consistent with the Pauli and Dirac matrices. Also has new diagrams (if you were reading the old version). As far a I'm concerned, the proof is complete; but I'll be re-arranging, adding a table of contents, etc.

It is interesting that GTR turns out to be an approximation only (1/gamma <> 0 unless c = 0 - i.e., no initial condition ), since the Fundamental equation of STR covers all possible real numbers, so it really is a mathematical analysis rather than a physics one (I have provided interpretations of various perspectives - QM, GTR, etc.
BuleriaChk

Posts: 11
Joined: Sat Mar 11, 2017 7:59 pm

### Re: Relativity, Fermat's Last theorem, and the Binomial Theo

Major Update to "The Relativistic Unit Circle: (my core document)

1. added Table of Contents with Bookmarks to more easily understand the flow of ideas.
2. added list of references and links to other pdf's on my website.
3. add a discussion of Pythagorean Triples as group (which further nails Fermat's Theorem), and the Lorentz transform to include relativistic energy, to show why Einstein rejected the Lorentz Transform in STR....
BuleriaChk

Posts: 11
Joined: Sat Mar 11, 2017 7:59 pm