# Thread: Proof of Fermat's Theorem using vectors

1. ## Re: (Another) Proof of Fermat's Theorem (which is actually the same)

Originally Posted by BuleriaChk
Neither Grapes or the Naked Emperor have gotten to the point in their studies where manknind has invented the wheel.
Or even the square. They only think in one dimension, clapping sticks together to measure them....
(John Gabriel had that problem as well....)

Even the Greeks knew about the circle....

But the Relativistic circle, and the characterization of integer generation by Lorentz rotation is at the foundation of sampling theory, signal processing and analysis and analysis, (For the Lorentz Boost, imagine that the invariant initial condition ct is replaced by Planck's constant, and then ask yourself what happens to and h as goes to infinity.
I pointed out your many errors, you ignored them all. Instead, you produced the above rant.

You are being a troll. Find another playground.

2. ## Re: (Another) Proof of Fermat's Theorem (which is actually the same)

Originally Posted by grapes
I pointed out your many errors, you ignored them all. Instead, you produced the above rant.

You are being a troll. Find another playground.
-----------------------------------------------
The only errors you pointed out were trivial typos because I don't have a proofreader and was writhg a lot of tex in the equations. (I was trying to understand these concepts in real time, and you jumped in before I had a chance to correct them myself). But thank you for that, anyway. All your other statements were donkey braying, spamming my thread, along with others to try to drown me out.

We'll see if your position is correct. There are others reading this forum and the documents on my website.
Time will tell, and our positions are on record for all to see.
------------------------------------------------

The result of my analysis is the Proof of Fermat's theorem by the relativistic unit circle, where the orthogonal axes are characterized for two independent sets independent real numbers related by the equality triangle, with the Pythagorean triples a special case. (substitue (x,y) or (a,b) for (c,v) with all elements variable on the axes.)

Try to understand the relativistic unit circle, in which I re-invent the wheel (the general equation of a circle in two dimensions in real numbers with ct' being the "final state" in the diagram on the left, where the Pythagorean circle is inscribed in the relativistic unit circle as a special case of integers). The "final" state is then characterized with the same equation where ct is now the "intial" state.

I then show how Lorentz rotations generate unit integers which leads to the fact that the Lorentz boost cannot be an integer (the integers are craeated only along the horizontal and vertical axes in the positive quadrant).

The analysis is consistent with the vector analysis in this thread (I may have to clean it up a bit, but the proof should be clear from the RUC)

This analysis is fundamental to sampling by the Dirac delta function in signal processing and analysis, and important for understanding normalization in Quantum Field Theory.

3. ## Re: (Another) Proof of Fermat's Theorem (which is actually the same)

Originally Posted by grapes
Originally Posted by BuleriaChk
There are now 4 elements: on the lhs, with three integers: , and 2ab - on the r.h.s., so cannot be an integer used to construct Fermat's equation since all the Pythagorean triples require that 2ab = 0. This also follows from the vector analysis and the relativistic unit circle. So c cannot be part of a Pythagorean triple in the Binomial Expansion for the case n=2, and thus is not an integer.

The Binomial theorem is valid for all n > 2 where rem(a,b,n) > 0. Fermat's Theorem is proved; c is not an integer, so is not an integer.
Nonsense

By definition, a Pythagorean triple is three nonzero integers a,b,c such that , so 2ab is *never* zero.

This has been pointed out before, and you keep ignoring it.

Well, you've said c=a+b, so of course a,b,c is not a Pythagorean triple--they don't satisfy the Triangle Inequality. But, c is an integer, it's equal to a+b
Originally Posted by grapes
Originally Posted by BuleriaChk
Neither Grapes or the Naked Emperor have gotten to the point in their studies where manknind has invented the wheel.
Or even the square.
I pointed out your many errors, you ignored them all. Instead, you produced the above rant.

You are being a troll.
This has been all of our experience with BulariaChK and the sheer frustration of trying to get him to see his errors.
When shown them, he usually weasels, Insults or Ignores. Then he throws out some Tangent Circus side show distraction to get attention away from the confrontation of the error that he never addresses.

Originally Posted by BuleriaChk
I can't believe the urban legend that no-one has proven Fermat's theorem isn't a fricken joke on all of us .....
And there you have it. BulariaChK has fallen into the same trap so many others do:
https://arxiv.org/ftp/math/papers/9810/9810027.pdf
Fermat's Last Theorem is Solved
proposed elementary proof of Fermat's last theorem | planetmath.org
Chuck is not original... nor alone in making these same mistakes.
And what most of them do when shown the errors? They ignore them. They don't want to believe that thing they spent so much time working on failed.
And most of them all think they were the first or only ones to think of it.
Which is a fallacy in itself- since as most of them point out, the idea is elementary and simple.

4. ## Re: (Another) Proof of Fermat's Theorem (which is actually the same)

Originally Posted by Neverfly
This has been all of our experience with BulariaChK and the sheer frustration of trying to get him to see his errors.
When shown them, he usually weasels, Insults or Ignores. Then he throws out some Tangent Circus side show distraction to get attention away from the confrontation of the error that he never addresses.

And there you have it. BulariaChK has fallen into the same trap so many others do:
https://arxiv.org/ftp/math/papers/9810/9810027.pdf
Fermat's Last Theorem is Solved
proposed elementary proof of Fermat's last theorem | planetmath.org
Chuck is not original... nor alone in making these same mistakes.
And what most of them do when shown the errors? They ignore them. They don't want to believe that thing they spent so much time working on failed.
And most of them all think they were the first or only ones to think of it.
Which is a fallacy in itself- since as most of them point out, the idea is elementary and simple.
The problem is solved by the relativistic unit circle and its relation to the Binomial Theorem.

(I don't claim to be original, but none of the proofs you listed mention the relativistic unit circle with the Lorentz boost being the source of the interaction term, or even the idea that a and b must be independent variables. The rest of your post is an appeal to urban legend as an authority ....

But thanks for the links... they may be consistent with mine or not... (I am not about to try to discredit them, I have my hands full here. (From what I can tell, some of them are close, but not quite there....)

Time will tell.... there are a lot of people reading this forum and my website, so there must be a literature search going on elsewhere.... keep searching yourself, and see if you can find one that mentions the RUC.

And if anyone does find such a link, send it to me so I can congratulate the author.

(I finally contacted the head of the math dept. at UCSB, who suggested I submit it to a math journal, but they'll hear about it anyway if I'm right, and I would be happy to put into publishable form for their journals if asked....) And I'm still trying to talk him into presenting it to someone at UCSB over beer and pizza...

Note on vectors:

Real operations on a set of real numbers in a single dimension as coefficients of a vector means that and refer to the same unique number for single valued functions. That is, the coefficient in a single dimension represents a single number line for real numbers.

(my proof of Fermat's Theorem depends on two dimensions (a, b); the Binomial Theorem also depends on two dimensions in real numbers (x,y), and is shown to be complete by the application of the RUC with Pythagorean triplets a special case of a triangle inscribed in the general form of the RUC "real number dilation" equation; (in this context, a "real number" creation relationship in two dimensions.

in the real number plane characterized by (x,y), where x and y are both variables on independent Cartesian axes.

For the case in which xt' is a final condition vs the case where xt is an initial condition.

In this interpretation, t and t' can be thought of as relative "number" densities.

5. ## Re: (Another) Proof of Fermat's Theorem (which is actually the same)

Originally Posted by BuleriaChk
The problem is solved by the relativistic unit circle.

(I don't claim to be original, but none of the proofs you listed mention the relativistic unit circle with the Lorentz boost being the source of the interaction term, or even the idea that a and b must be independent variables.

The rest of your post is an appeal to urban legend as an authority ....

But thanks for the links... they may be consistent with mine or not... (I am not about to try to discredit them, I have my hands full here.)

time will tell.... there are a lot of people reading this forum and my website, so there must be a literature search going on elsewhere.... keep searching yourself, and see if you can find one that mentions the RUC.

And if anyone does find such a link, send it to me so I can congratulate the author.

(I finally contacted the head of the math dept. at UCSB, who suggested I submit it to a math journal, but they'll hear about it anyway if I'm right, and I would be happy to put into publishable form for their journals if asked....) And I'm still trying to talk him into presenting it to someone at UCSB over beer and pizza...
Instead of posting here, you should be working on that math paper. You don't trust us anyway.

Go, get it published, get world acclaim. Why are you wasting time here? Go, we'll be rooting for you.
Note on vectors:

Real operations on a set of real numbers in a single dimension as coefficients of a vector means that and refer to the same unique number for single valued functions. That is, the coefficient in a single dimension represents a single number line for real numbers.

(my proof of Fermat's Theorem depends on two dimensions (a, b); the Binomial Theorem also depends on two dimensions in real numbers (x,y), and is shown to be complete by the application of the RUC with Pythagorean triplets a special case of a triangle inscribed in the general form of the RUC "real number dilation" equation (in this context, a "real number" creation relationship in two dimensions.

in the real number plane characterized by (x,y), where x and y are both variables on independent Cartesian axes.

For the case in which xt' is a final condition vs the case where xt is an initial condition.

In this interpretation, t and t' can be thought of as relative "number" densities.

6. ## Re: (Another) Proof of Fermat's Theorem (which is actually the same)

The Whole Story

One of the reasons why Fermat’s Last Theorem is so difficult to prove is that it applies to an infinite number of equations: xn + yn = zn, where n is any number greater than 2. Even the advent of computers was of no help, because, although they could be employed to help perform sophisticated calculations, they could at best deal with only a finite number of equations.

Soon after the Second World War computers helped to prove the theorem for all values of n up to five hundred, then one thousand, and then ten thousand. In the 1980’s Samuel S. Wagstaff of the University of Illinois raised the limit to 25,000 and more recently mathematicians could claim that Fermat’s Last Theorem was true for all values of n up to four million. In other words, for the first four million equations mathematicians had proved that there were no numbers that fitted any of them.

This may seem to be a significant contribution toward finding a complete proof, but the standards of mathematical proofs demand absolute confidence that no numbers fit the equations for all values of n. Even though the theorem had been proven for all values n up to four million, there is no reason why it should be true for n = 4,000,001. And if in the future supercomputers proved the theorem for all values n up to one zillion, there is no reason why it should be true for n = one zillion and one. And so on ad infinitum. Infinity is unobtainable by the mere brute force of computerised number crunching.

The mathematician’s desire for an absolute proof up to infinity may seem unreasonable, but the case of Euler’s conjecture demonstrates the necessity of unequivocal truth. The 17th century Swiss mathematician Leonhard Euler claimed that there are no whole number solutions to an equation not dissimilar to Fermat’s equation:

Euler’s equation: x4 + y4 + z4 = w4

For two hundred years nobody could prove Euler’s conjecture, but on the other hand nobody could disprove it by finding a counter-example. First manual searches and then years of computer sifting failed to find a solution. Lack of a counter-example appeared to be strong evidence in favour of the conjecture. Then in 1988 Noam Elkies of Harvard University discovered the following solution:

2,682,4404 + 15,365,6394 + 18,796,7604 = 20,615,6734

Despite all the previous evidence, Euler’s conjecture turned out to be false. In fact Elkies proved that there are infinitely many solutions to the equation. The moral of the story is that you cannot use evidence from the first million numbers to prove absolutely a conjecture about all numbers.

7. ## Re: (Another) Proof of Fermat's Theorem (which is actually the same)

No mention of the Relativistic Unit Circle. (Not only that, but I only require evidence from the first three numbers...

I would add links to my recent PDF's to my original thread so that new readers can reference them, but Grapes has closed it in an effort to silence me. There are over 11,366 views of the thread....

I don't care if Grapes closes his own thread, but to close mine is unconscionable.

Time will tell for my proof, in any case.

Keep searching (it would help a lot if you knew or understood what you are looking for) ....

8. ## Re: (Another) Proof of Fermat's Theorem (which is actually the same)

Originally Posted by BuleriaChk
No mention of the Relativistic Unit Circle. (Not only that, but I only require evidence from the first three numbers...

I would add links to my recent PDF's to my original thread so that new readers can reference them, but Grapes has closed it in an effort to silence me. There are over 11,366 views of the thread....

I don't care if Grapes closes his own thread, but to close mine is unconscionable.

Time will tell for my proof, in any case.

Keep searching (it would help a lot if you knew or understood what you are looking for) ....
I know mathematics more than you so why do you not follow your own advice little boy?

9. ## Re: Proof of Fermat's Theorem using vectors

Originally Posted by emperorzelos
I know mathematics more than you so why do you not follow your own advice little boy?
Empty braggadocio from a Village Idiot....

10. ## Re: Proof of Fermat's Theorem using vectors

Originally Posted by BuleriaChk
Empty braggadocio from a Village Idiot....
NOt at all, working on a Ph.D in mathematics and have a masters degree in mathematics, I did my thesis in abstract algebra. What have you done in higher mathematics?

I can say my education include Functional analysis where dealing with finite dimension is rare and most spaces are infinite dimensional AND In module theory I deal with things where the concept of dimension is meaningless.

What have you done beyond elementary linear algebra?

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