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 April 27th, 2019, 09:15 AM #11 Member   Joined: Mar 2019 From: california Posts: 74 Thanks: 0 I finally got the photo posted. If you accept the equation Z^n = X^n +Y^n, then X^2 + Y^2 < Z^2. While we don't know how much X^2 + Y^2 is less than Z^2, we can assign a variable, e/f, to represent this unknown. So, X^2 + Y^2 = e/f * Z^2. The range of e/f is between 1 and 2^1/2. All your questions refer to using a ratio e/f = 1, which is true for the case when n = 2. i.e. X^2 + y^2 = z^2 (WHEN TALKING ABOUT TRIPLETS), in this case we are talking about how much smaller X^2 + Y^2 are to Z^2 when Z^n = X^n + Y^n. IMG_6049 (1).jpg Last edited by skipjack; April 27th, 2019 at 03:41 PM.
April 27th, 2019, 11:56 AM   #12
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Quote:
 Originally Posted by michaelcweir If you accept the equation Z^n = X^n +Y^n,
WEIRd looking equation

Last edited by skipjack; April 27th, 2019 at 03:40 PM.

April 27th, 2019, 03:46 PM   #13
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Quote:
 Originally Posted by michaelcweir I finally got the photo posted.
I don't see what relevance it has to FLT.

Your first couple of posts at least stated complete arguments. Lately nothing you write makes sense at all.

I don't follow your calculation in the diagram. And one of the denominators is unclear, is it n^2? Or x^2 or z^2?

 April 27th, 2019, 04:04 PM #14 Global Moderator   Joined: Dec 2006 Posts: 20,926 Thanks: 2205 That denominator appears to be x². I've no idea why x and y sometimes appear instead of X and Y for no apparent reason.
 April 27th, 2019, 05:01 PM #15 Member   Joined: Mar 2019 From: california Posts: 74 Thanks: 0 I think if you inspect the diagram photo I just uploaded, you will understand where where the Xaand Y's come from.
April 27th, 2019, 05:10 PM   #16
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 Originally Posted by michaelcweir I think if you inspect the diagram photo I just uploaded, you will understand where where the Xaand Y's come from.
Ok you proved that $z^{n - 2} < x^{n-4} + y^{n-4}$. You didn't prove that $x^2 + y^2 < z^2$. How does this relate to FLT?

Quote:
 Originally Posted by michaelcweir If you accept the equation Z^n = X^n +Y^n, then X^2 + Y^2 < Z^2.
I don't think this is true. Take $2^5 + 3^5 = z^5$. Then $z = 275^{\frac{1}{5}} \approx 3$.

But $2^2 + 3^2 = 13$ and $3^2 = 9$. And nothing you wrote uses the fact that $x$, $y$, and $z$ are integers. So here's a counterexample to your claim.

Last edited by Maschke; April 27th, 2019 at 05:56 PM.

April 28th, 2019, 03:21 PM   #17
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Quote:
 Originally Posted by Maschke Ok you proved that $z^{n - 2} < x^{n-4} + y^{n-4}$. You didn't prove that $x^2 + y^2 < z^2$. How does this relate to FLT? o, x2+y2
The counter-example only shows that my notation for less than was the wrong one. You are correct that Z^2 < X^2 + Y^2. Fortunately, I assigned the right variable range and so the calculation was correct. The diagram also shows the right relationship between Z^2 and X^2 + Y^2. So thank you for catching the error. You did demonstrate the right inequality. So if you assign a variable, e/f, you can make the calculation and show that Y can never be an integer.

Last edited by skipjack; April 28th, 2019 at 05:42 PM.

May 6th, 2019, 05:00 PM   #18
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Here is 3 pages showing how Y id determined to be between 0.48 and 1.
Attached Images
 IMG_6061.jpg (84.4 KB, 6 views) IMG_6062.jpg (82.3 KB, 6 views) IMG_6063.jpg (85.5 KB, 4 views)

May 6th, 2019, 05:06 PM   #19
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here is page 1 of 3
Attached Images
 IMG_6061.jpg (84.4 KB, 2 views)

May 6th, 2019, 05:27 PM   #20
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working out value for Y in terms of h,c/d and e/f

here are 3 pages of handwritten analysis
Attached Files
 fermat one20190506_18185751.pdf (9.4 KB, 3 views) fermat two20190506_18224429.pdf (8.5 KB, 2 views) fermat three20190506_18243424.pdf (7.7 KB, 1 views)

 Tags analysis, diophantine, diopphantine, fermat, theorem

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