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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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 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 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Lourie Number Theory 3 April 1st, 2017 12:37 AM McPogor Number Theory 5 December 7th, 2013 07:28 PM mathbalarka Number Theory 2 April 3rd, 2012 11:03 AM theomoaner Number Theory 29 November 26th, 2011 10:23 PM SnakeO Number Theory 10 September 25th, 2007 04:23 PM

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