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

1. ## Re: Proof of Fermat's Theorem

Originally Posted by BuleriaChk

-------------------------------
case n=2
--------------
ab=0 (Pythagorean Triple

,

,
--------------------------------

, ,
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
Math is not your strong suit.

2. ## Re: Proof of Fermat's Theorem

Originally Posted by grapes
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.
No shit, Dick Tracy.

(check the cross product where a and b commute in my pdf)....

Now all you have to do is imagine n>2....

3. ## Re: Proof of Fermat's Theorem

Originally Posted by BuleriaChk
Originally Posted by grapes
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.
No shit, Dick Tracy.
And yet, you say in your post, that it is *not equal* to zero
(check the cross product where a and b commute in my pdf)....

Now all you have to do is imagine n>2....

4. ## Re: Proof of Fermat's Theorem

Originally Posted by grapes
And yet, you say in your post, that it is *not equal* to zero
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).

5. ## Re: Proof of Fermat's Theorem

Originally Posted by BuleriaChk

Look how you defined these vectors! See above
Originally Posted by BuleriaChk
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.
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).

6. ## Re: Proof of Fermat's Theorem

Originally Posted by grapes
Look how you defined these vectors! See above

No, their dot product is always zero.

,
,

,

,

is the angle between the vectors (for those who are just beginning high school math).

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

Originally Posted by BuleriaChk

This is how you defined these vectors, a and b are positive integers.
Originally Posted by BuleriaChk
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.
The dot product will always be zero. That means will *never* equal .

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

Originally Posted by grapes
This is how you defined these vectors, a and b are positive integers.

The dot product will always be zero. That means will *never* equal .
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 ....

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]"

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

Originally Posted by BuleriaChk
Hey, you may be on to something, Dick Tracy..
I was just pointing out one of the mistakes that invalidate your "proof" of Fermat's Last Theorem.

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

Originally Posted by grapes
I was just pointing out one of the mistakes that invalidate your "proof" of Fermat's Last Theorem.
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...

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