April 30th, 2019, 11:07 AM  #21 
Member Joined: Mar 2019 From: california Posts: 74 Thanks: 0 
You will have to show how that qapplies.

April 30th, 2019, 01:35 PM  #22 
Member Joined: Mar 2019 From: california Posts: 74 Thanks: 0 
Thank you for waiting for a reply. I felt it was more important to reply to Masche about the other Fermat's theorem. Now that he has agreed that f/l is greater then 1, the proof is very straightforward, being a simple manipulation of an equation. Then when you substitute the ranges in for the different ratios I am reasonably certain that he has already done every check that he can think of to come up with a counter example. If it was me, with his connections, I would be contacting other mathematicians to see what they could come up with. It's all over except for the shouting. If you looked at Masche's reply below, he stated exactly what the the answer should be to your first question. The second part of your reply is whether X^n/2 will get smaller than X^2? And the answer is that it won't, not that it can't but that it would violate the definition of what the Pythagorean theorem means. To do the next iteration and keeping the X^n/2 leg the same would mean that The end point of the X leg would extend past the endpoint of the Z leg. So yes, there is an end to the iterations that can be achieved. The idea of infinite number of them is only due to the fact that the value of n is unknown..As soon as we know n, we can determine how many iterations to make. 
April 30th, 2019, 03:13 PM  #23  
Senior Member Joined: Aug 2012 Posts: 2,355 Thanks: 737  Quote:
Quote:
Still, I asked you to rewrite your clearly and with whatever modifications are needed now that you realize you had your inequality backward. That's a fair request. Also, aren't you curious to go through your own argument to see how you arrived at the wrong inequality? When I went through your argument I found that it didn't even prove the WRONG inequality. Your argument didn't prove what you said it did. You should go back through your work and see where you went wrong. Quote:
In this case I did spend some time on it. I'm not saying I wouldn't in the future. I've just run out of interest. I don't feel like going through the algebra. Also as I mentioned, someone else early on pointed out an error in your algebra which you neither acknowledged nor corrected. Anyway no, I haven't looked for counterexamples and I also haven't thoroughly analyzed the inequality. I just ran out of steam for this little project. But a clear rewrite, line by line, and taking into account the errors that have already been found, would be helpful to me and to others. Quote:
You haven't got a proof. Your certainty is unwarranted. Quote:
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This refers to SDK's remark that the padic numbers show that your proof can't be right. Here's what he was referring to. Mathematicians study all kinds of different number systems. One class of them is the padic numbers. We don't need the details here but they are important in number theory. In fact Wiles's proof of FLT heavily uses them It turns out that in the padic numbers there are FLT triples, thus making FLT false. However, the padic numbers have a lot of the same algebraic properties as the regular old integers. So that if you have an alleged proof of FLT based on elementary algebraic manipulation, it must be wrong, since it would equally well apply to the padics. Theres a Quora thread on this: https://www.quora.com/WhatifIfoun...slasttheorem I'll quote the relevant part. Quote:
Last edited by Maschke; April 30th, 2019 at 03:26 PM.  
April 30th, 2019, 06:37 PM  #24  
Senior Member Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
Quote:
 
May 6th, 2019, 05:32 PM  #25 
Member Joined: Mar 2019 From: california Posts: 74 Thanks: 0 
i posted handwritten analysis, but I had to upload 3 times before it was readablea s pdf.

May 6th, 2019, 05:34 PM  #26 
Member Joined: Mar 2019 From: california Posts: 74 Thanks: 0 
It's in the other proof.

May 6th, 2019, 05:34 PM  #27  
Senior Member Joined: Aug 2012 Posts: 2,355 Thanks: 737  Quote:
Or you can pick up a bit of Mathjax. Just hit the Quote button to see how I did this: $x^n + y^n = z^n$ But even without that, just straightforward ASCII is fine. x^n + y^n = z^n That's a million times better than trying to decode a handwritten exposition. Last edited by Maschke; May 6th, 2019 at 05:37 PM.  
May 19th, 2019, 01:19 PM  #28 
Member Joined: Mar 2019 From: california Posts: 74 Thanks: 0 
Hi Masche I'm doing my best to comply with your request. I decided the best way to do that is to follow Fermat's example. Which is to give you the bare minimum to solve the proof. I have posted 2 diagrams the use of the Nautilus process to determine that Z, for any n greater than 2, must be less than y+1. Since Z must be greater than Y, Y<Z<Y+1. Thus Z must be irrational. This proves FLT.. from fig. 2 Z^2 +X^2 < X^2 +(Y+1)^ 2 This implies Z^2 < (Y+1)^2 OR z < y+1 
May 19th, 2019, 02:27 PM  #29 
Senior Member Joined: Mar 2019 From: iran Posts: 318 Thanks: 14 
z can be greater than y+1 for example 28^10 + 30^10 = (31.24)^10 31.24 is greater than 30+1 you are begging the question in fig 2 you assume side z is smaller than side y+1 then you get z is smaller than y+1 
May 20th, 2019, 01:06 PM  #30 
Member Joined: Mar 2019 From: california Posts: 74 Thanks: 0 
Yes that is certainly true. But it also is true that 31.24 is not an integer. If you say Z^n is an integer and Z^n = X^n + Y^n, then Z^n <X^n +(Y+!)^n in every case. This is true whether any of X,Y< or Z is rational or not. Y + 1 is clearly larger than Y. See if you can find a better counter example. You would have made me sit up if you had said Z =31, and it was true. The issue is not whether Y < Z < Y +1 only, but also that both Y and Z are integer. So your example is outside the criteria that Z^n be integer. Let me give you an example that Maschke and I both used. 3^2 + 4^2 =5^2, but 3^3 +4^3 = 4.1^3 approximately, not 5^3. Y+1 in this case is 5. It took me a while to understand the distinction. 

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