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- 03-18-2017, 11:19 AM #161
## Re: Proof of Fermat's Theorem

The vectors a and b are perpendicular to each other, so of course their dot product is *equal* to zero. But even that doesn't mean that 2ab equals zero.

Therefore, c' cannot be an integer

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

case n>2

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

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

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

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

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

QED

- 03-18-2017, 02:05 PM #162

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## Re: Proof of Fermat's Theorem

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"Flamenco Chuck" Keyser

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

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- 03-18-2017, 03:39 PM #163
## Re: Proof of Fermat's Theorem

- 03-18-2017, 06:21 PM #164

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## Re: Proof of Fermat's Theorem

The dot product is zero only if there is no interaction (multiplication) - (i.e. ). If there is interaction, then both the dot products and the cross product exists.

Pythagorean triples model no interaction. The Binomial Expansion**always**includes interaction.

Interaction means multiplication of two independent variables ab=ba (the factor of 2 exists because the variables commute).

Fermat's expression lacks multiplication, but his expression is only valid for n=2 if no interaction (multiplication) is involved (which is why he specified n>2 in his theorem).Last edited by BuleriaChk; 03-18-2017 at 06:29 PM.

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"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/27/2017 04:58 AM PST**

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

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- 03-18-2017, 10:20 PM #165
## Re: Proof of Fermat's Theorem

Look how you defined these vectors! See above

No, their dot product is always zero.

Pythagorean triples model no interaction. The Binomial Expansion**always**includes interaction.

Interaction means multiplication of two independent variables ab=ba (the factor of 2 exists because the variables commute).

Fermat's expression lacks multiplication, but his expression is only valid for n=2 if no interaction (multiplication) is involved (which is why he specified n>2 in his theorem).

- 03-18-2017, 10:53 PM #166

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## Re: Proof of Fermat's Theorem

Last edited by BuleriaChk; 03-18-2017 at 11:31 PM.

_______________________________________

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/27/2017 04:58 AM PST**

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

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- 03-19-2017, 05:49 AM #167
## Re: Fermat's last, and mine too.

- 03-19-2017, 09:16 AM #168

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## Re: Fermat's last, and mine too.

Hey, you may be on to something, Dick Tracy..

(That is why c can never be an integer unless it is part of a Pythagorean Triple.... in the general Binomial Expansion for the case n=2. )

But the equation is true for all real numbers.

What does it mean for ? (think**Cartesian Coordinate system - Wiki article)**

Well, ok, that may too complex**Math Is Fun**

(Play with the interactive graph awhile... it might help you as an introduction to more advanced math)..

(if you get confused about the Binomial Expansion, scroll down to the bottom where they introduce three dimensions).

Then go back to the Wiki article....

(Hint: the set {c,a,b,2ab} is not a triangle. Neither is the set {z,x,y,2xy},

Then consult the institution that taught you your advanced math and physics and see if you can get a refund ....

**(Follow, Follow the links,**and they will lead you to freedom... some day... maybe...)

**From the Wiki article (w.r.t. John Gabriel)"**

"**The development of the Cartesian coordinate system would play a fundamental role in the development of the Calculus by Isaac Newton and Gottfried Wilhelm Leibniz.**.^{[3]}The two-coordinate description of the plane was later generalized into the concept of vector spaces^{[4]"}Last edited by BuleriaChk; 03-19-2017 at 11:24 AM.

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/27/2017 04:58 AM PST**

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

**Ignore List -The Peanut Gallery.**

- 03-19-2017, 10:27 AM #169
## Re: Fermat's last, and mine too.

- 03-19-2017, 10:51 AM #170

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## Re: Fermat's last, and mine too.

**Doesn't invalidate the proof at all. The proof specifies n>2.**The dot product is only valid for for the Pythagorean triple.

It is NOT valid for terms in rem(a,b,n) for n>2 Consider the case n=3, which has terms like and

In the terms containing products of a and b ( ), and , are NEVER orthogonal, and rem(a,b,3) only vanishes if a = 0 or b= 0.

(the terms only intersect at (0,0).

Village idiot...Last edited by BuleriaChk; 03-19-2017 at 11:18 AM.

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/27/2017 04:58 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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