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- 12-25-2016, 05:43 AM #11

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- 12-25-2016, 05:53 AM #12
## Re: Proof of Fermat's Theorem using vectors

- 12-25-2016, 06:08 AM #13

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- 12-25-2016, 06:19 AM #14
## Re: Proof of Fermat's Theorem using vectors

- 12-25-2016, 07:32 PM #15

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## (Another) Proof of Fermat's Theorem (which is actually the same)

The context of the analysis below can also be compared with the relativistic approach in which rem(a,b,2) corresponds to a Lorentz "boost" in addition to a Lorentz rotation for two integers.

**The Relativistic Unit Circle**

is the Binomial Expansion for the case n=2.

is the equation of a circle.

let r, x, and y be integers, a=x, b=y, c=r.

is the equation of all Pythagorean circles where the radius c is an integer and the sides a and b form a Pthagorean right triangle within the circle.

If the graph is not a circle, the Binomial expansion yields

for the case n=2, which is the equation of a Pythagorean circle and a rectangle of area = 2ab

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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.

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I can't believe the urban legend that no-one has proven Fermat's theorem isn't a fricken joke on all of us .....Last edited by BuleriaChk; 12-26-2016 at 06:05 AM.

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"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**

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- 12-25-2016, 10:29 PM #16

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- 12-26-2016, 06:01 AM #17

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

I have added a connection to Fermat's theorem to my discussion of the relatavistic unit circle at:

**Relativistic Unit Circle**

which shows the connection to both the Pythagorean circle and the Binomial Theorem (via a Lorentz "boost")

It shows that the proof of Fermat's Theorem from STR and the Lorentz transform is consistent with that of the Binomial theorem.

In particular, the Lorentz "boost" at is consistent with the requirement of the Binomial Therorem that for a Pythagorean triple (or any triangle inscribed in the Relativistic unit circle, since and are independent (orthogonal) in the first (positive) quadrant.

The vector analysis from the OP is still being added to the pdf at present, but is not necessary, as the relation is clear geometrically.Last edited by BuleriaChk; 12-26-2016 at 06:17 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.**

- 12-26-2016, 08:18 AM #18

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

- 12-26-2016, 11:19 AM #19
## Re: (Another) Proof of Fermat's Theorem (which is actually the same)

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.

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.

---------------------

I can't believe the urban legend that no-one has proven Fermat's theorem isn't a fricken joke on all of us .....Last edited by grapes; 12-26-2016 at 11:21 AM.

- 12-26-2016, 11:47 AM #20

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

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.Last edited by BuleriaChk; 12-26-2016 at 01:02 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.**

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