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 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  WEIRd looking equation Last edited by skipjack; April 27th, 2019 at 03:40 PM. 
April 27th, 2019, 03:46 PM  #13 
Senior Member Joined: Aug 2012 Posts: 2,355 Thanks: 737  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  
Senior Member Joined: Aug 2012 Posts: 2,355 Thanks: 737  Quote:
Quote:
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  
Member Joined: Mar 2019 From: california Posts: 74 Thanks: 0  Quote:
Last edited by skipjack; April 28th, 2019 at 05:42 PM.  
May 6th, 2019, 05:00 PM  #18 
Member Joined: Mar 2019 From: california Posts: 74 Thanks: 0 
Here is 3 pages showing how Y id determined to be between 0.48 and 1.

May 6th, 2019, 05:06 PM  #19 
Member Joined: Mar 2019 From: california Posts: 74 Thanks: 0 
here is page 1 of 3

May 6th, 2019, 05:27 PM  #20 
Member Joined: Mar 2019 From: california Posts: 74 Thanks: 0  working out value for Y in terms of h,c/d and e/f
here are 3 pages of handwritten analysis


Tags 
analysis, diophantine, diopphantine, fermat, theorem 
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