My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Thanks Tree65Thanks
Reply
 
LinkBack Thread Tools Display Modes
June 15th, 2019, 04:26 PM   #81
Senior Member
 
Joined: Aug 2012

Posts: 2,343
Thanks: 732

Quote:
Originally Posted by topsquark View Post
Do you actually know what p-adics are? And how to apply them? Don't just feed me the google stuff. Give me some good context.
I don't think this is a fair or relevant challenge. The point is only that there's a number system, the p-adics, that obeys all the usual laws of arithmetic, but that contains Fermat triples. One doesn't need to know anything about the p-adics (which are typically unknown even to undergrad math majors) to understand this point.

The argument is referenced here in the answer of nguyen quang do.
Maschke is offline  
 
June 15th, 2019, 06:36 PM   #82
Senior Member
 
Joined: Oct 2009

Posts: 841
Thanks: 323

Quote:
Originally Posted by michaelcweir View Post
Yes I did reply to Hensel's Lemma to several people in several ways, including to Maschke,. He never did reply.
Recently he said he wasn't an expert, so maybe that is why..
But you say you have understood Hensel's Lemma, so let me ask you what I asked him, perhaps in more detail.

While I did not plow through the Lemma, I did understand it to be a generalization of modular systems..

For example, solving an algebraic equation for Y and the answer is Y=3 mod 1, would mean a p-adics. of the universe of integer numbers, both positive and negative. So if you were to attempt to solve Y when the answer for Y is something other than an integer (Y=0.5, for example), Hensel's Lemma says you don't even need to check the calculation for correctness as the Lemma says that it will be wrong. And you would be right in asserting that.

So that's what everybody's claim is that because I have p-adics statements in the proof, it must be wrong. But these people are missing 2 pieces of the lemma that they are missing.

First there are mathematical statements that are not p-adics. For instance the intersection of 2 Venn circles is not a p-adics. Essentially, Wile's proof of FLT is an elaborate description of 2 circles intersecting (elliptic curves). By the way, my proof is the same. Venn circles are a visual statement of an mathematical expression, so you can substitute a mathematical formula for a circle.

Second, in order to apply Hensel's Lemma, it is important to examine each and every statement to see if it is p-adics. Failure to to do that means that the lemma cannot be applied. That failure means that you would have to examine statement of the proof in order to determine if it was a good proof or not. The lemma is irrelevant in this case.

Wile's proof has a t least one p-adics statement in the proof. Because it has another algebraic expression, Hensel's Lemma has to be excluded whether the proof is valid or not.

So that 's the question I asked Maschke and now you. Is every statement in my proof a p-adics statement or not? If there is even on statement that is different from a p-adics, then the lemma cannot be applied. As I told Maschke, those statements necessary fopr the proof are in the proof.
So you understand that if each step in your proof is a simple algebraic manipulation, then the proof would be wrong? So then the question becomes: which step in your proof is NOT such a simple algebraic manipulation?
Micrm@ss is offline  
June 15th, 2019, 06:49 PM   #83
Senior Member
 
Joined: Oct 2009

Posts: 841
Thanks: 323

Never mind. I briefly checked the proof of the OP. Hensel's lemma doesn't apply. Not every step can be obviously modified to the p-adic numbers.

I'm still not bothering to deeply check the proof. Maybe if you write it down in a clean way with LaTeX...
Micrm@ss is offline  
June 15th, 2019, 07:23 PM   #84
Senior Member
 
Joined: Aug 2012

Posts: 2,343
Thanks: 732

Quote:
Originally Posted by Micrm@ss View Post
Never mind. I briefly checked the proof of the OP. Hensel's lemma doesn't apply. Not every step can be obviously modified to the p-adic numbers.
Interesting. Which steps? And which version of the proof?
Maschke is offline  
June 16th, 2019, 12:27 AM   #85
Senior Member
 
Joined: Oct 2009

Posts: 841
Thanks: 323

Quote:
Originally Posted by Maschke View Post
Interesting. Which steps? And which version of the proof?
Oh, there are different versions? I didn't realize. I'm talking about the OP.
The OP uses inequalities in a fundamental way:

Quote:
The range of values Y takes on is between 0.6 and 1.
But the p-adics do not form an ordered field. In fact, I know of no total order on them. This means that at least this part of the proof cannot be modified (trivially) to the p-adic realm.

I'd need to study the proof more indepth to make sure. But I'm not going to bother at this moment since there isn't even a final version, nor a clean file to read.
Micrm@ss is offline  
June 16th, 2019, 07:07 PM   #86
Senior Member
 
Joined: Aug 2012

Posts: 2,343
Thanks: 732

Quote:
Originally Posted by Micrm@ss View Post
Oh, there are different versions? I didn't realize. I'm talking about the OP.
There are two separate threads, each containing multiple versions of the proof. They are not reworkings of the same idea. Some are different ideas. But if the p-adics don't disqualify the proof(s), @michael should post one official definitive proof so that we can all be talking about the same thing.


@michael if you want feedback that's what people need. A definitive and preferably marked-up version of your proof. You've noted several times that I've stopped giving specific suggestions. It's because every time I ask you a technical question you ignore it and post yet another version of your proof. This is frustrating to me. I hope you take these comments to heart. Post an official version written clearly enough that we can all follow it line by line.
Thanks from Denis

Last edited by Maschke; June 16th, 2019 at 07:10 PM.
Maschke is offline  
June 18th, 2019, 05:35 PM   #87
Member
 
Joined: Mar 2019
From: california

Posts: 68
Thanks: 0

Yes Maschke, I understand your frustration because I have it from from a different perspective.

When it became obvious that you did not understand what I thought were simple statements, I thought that I could use the nautilus construction to help explain it better. But it quickly became apparent that would not work either.

The written proof has always been the same.The April 19th posting is in the form you requested. When you complained about that I rewrote by hand and submitted it May 6th, 2019.You complained about that. So given my past experience with your requests, how do I know if you will come up with another objection or not?

Youngmath was able to read to at least line 4, where he found an error.I submitted the correction on June 6th, 2019.there's only a total number of 8 lines of equations.

I have made a few attempts to convert the proof to Latex, but have not been successful to date. i will make another attempt.
michaelcweir is offline  
June 18th, 2019, 07:30 PM   #88
Senior Member
 
Joined: Aug 2012

Posts: 2,343
Thanks: 732

Quote:
Originally Posted by michaelcweir View Post
Yes Maschke, I understand your frustration because I have it from from a different perspective.

When it became obvious that you did not understand what I thought were simple statements, I thought that I could use the nautilus construction to help explain it better. But it quickly became apparent that would not work either.

The written proof has always been the same.The April 19th posting is in the form you requested. When you complained about that I rewrote by hand and submitted it May 6th, 2019.You complained about that. So given my past experience with your requests, how do I know if you will come up with another objection or not?

Youngmath was able to read to at least line 4, where he found an error.I submitted the correction on June 6th, 2019.there's only a total number of 8 lines of equations.
Youngmath's contributions have been far more useful than mine. He's been able to follow more of your notation than I have.

Quote:
Originally Posted by michaelcweir View Post
I have made a few attempts to convert the proof to Latex, but have not been successful to date. i will make another attempt.
Any forum or site or journal you ever show your proof to will demand clear markup. If you seek recognition, you will have to at some point make your peace with taking the time to learn $\LaTeX$. You can "Quote" any post on this site to see how they did their markup. That's the best way to learn, just grab the code from other people's posts. For example the Fermat equation is $a^n + b^n = c^n$. Just hit Quote to see how I did that.

Last edited by Maschke; June 18th, 2019 at 08:06 PM.
Maschke is offline  
June 20th, 2019, 04:22 PM   #89
Member
 
Joined: Mar 2019
From: california

Posts: 68
Thanks: 0

Maschke
Any forum or site or journal you ever show your proof to will demand clear markup. If you seek recognition, you will have to at some point make your peace with taking the time to learn LATEX. You can "Quote" any post on this site to see how they did their markup. That's the best way to learn, just grab the code from other people's posts. For example the Fermat equation is an+bn=cn. Just hit Quote to see how I did that.

I did that but when i copied into the reply it was not translated into readable text. It still retained the $ sign.

I tried Latex but am having trouble getting brackets right. The purpose for sending this anyway is that you asaid previously that you accepted this part of proof, but then said you didn;t knpow if it wqs right or not. You never did rewpond whether it was right or not. Would you now say whether it was right or not.
Attached Files
File Type: pdf 2fermat text20190620_17181205.pdf (5.5 KB, 7 views)
michaelcweir is offline  
June 20th, 2019, 06:48 PM   #90
Senior Member
 
Joined: Aug 2012

Posts: 2,343
Thanks: 732

Quote:
Originally Posted by michaelcweir View Post
you asaid previously that you accepted this part of proof, but then said you didn;t knpow if it wqs right or not. You never did rewpond whether it was right or not. Would you now say whether it was right or not.
I have no idea what this is about. As I've said, from my point of view, whether rightly or wrongly, you appear to have posted several different variations of your proof, and they don't all seem (to me) to be the exact same idea; rather, they are somewhat different from one another.

Can you please write out a complete argument so that your exposition stands alone? I cannot agree that I've ever accepted anything nor do I know what argument you are making.

Please just say what your idea is and what you intend to show and why that proves FLT. Start from scratch, pretend this is your first post. Lay it out so that someone can understand what you are trying to say.

* Also, are you trying to LaTeX here on this website? Or in some standalone LaTeX environment? The latter can be hard to get started on, whereas working in the composition window on this site generally works.

ps -- What does {}X mean? What is all that in the pdf? It looks pretty mangled at my end and since it's a pdf it must be mangled at your end too.

You don't have to use LaTeX by the way, if that's giving you trouble. What people need is legibility. I can't discern your argument from this pdf. Perhaps others can.

* "I did that but when i copied into the reply it was not translated into readable text. It still retained the $ sign."

Please describe exactly what you're doing. Copied from where? Are you in Microsoft Word or something? Describe clearly your entire workflow so that we can debug your markup issues.

* Also there is an incredibly cool site at https://www.codecogs.com/latex/eqneditor.php where you enter markup (without the dollar signs) and it renders the LaTeX. You can use it to build up your exposition one little bit at a time.

* And finally, some of this is coming back to me now. Your claim that c/d > 1 I believe I pointed out is false in general a while back. Can you please write a complete argument, clearly stating all your assumptions?
Thanks from Denis and topsquark

Last edited by Maschke; June 20th, 2019 at 06:59 PM.
Maschke is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
analysis, diophantine, diopphantine, fermat, theorem



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Fermat's last theorem Lourie Number Theory 3 April 1st, 2017 12:37 AM
About Fermat's Little Theorem McPogor Number Theory 5 December 7th, 2013 07:28 PM
Fermat's Last Theorem mathbalarka Number Theory 2 April 3rd, 2012 11:03 AM
More Fermat's Last Theorem. theomoaner Number Theory 29 November 26th, 2011 10:23 PM
Fermat's last theorem. SnakeO Number Theory 10 September 25th, 2007 04:23 PM





Copyright © 2019 My Math Forum. All rights reserved.