My Math Forum  

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

Number Theory Number Theory Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 30th, 2010, 02:17 AM   #1
Senior Member
 
Joined: Aug 2010

Posts: 158
Thanks: 4

Simple Proof of Fermat's Last Theorem and Beal's Conjecture

Attached is the proof.
Attached Files
File Type: doc \'s.doc (30.5 KB, 73 views)
MrAwojobi is offline  
 
December 30th, 2010, 04:14 AM   #2
Senior Member
 
Joined: Aug 2010

Posts: 158
Thanks: 4

Re: Simple Proof of Fermat's Last Theorem and Beal's Conject

A few phrases have been added to the new attachment to emphasize that n is an odd integer and A and B do not necessarily need to be integers after the transformation.
Attached Files
File Type: doc \'s.doc (31.5 KB, 45 views)
MrAwojobi is offline  
December 30th, 2010, 05:25 AM   #3
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Simple Proof of Fermat's Last Theorem and Beal's Conject

Quote:
Originally Posted by MrAwojobi
A and B do not necessarily need to be integers after the transformation.
As a result, the transformation fails: you have not shown that FLT implies Tijdeman-Zagier ("Beal"), because FLT relies crucially on the assumption that the numbers are integers. Otherwise there are uncountably many (actually, ) counterexamples. For example,

Your FLT proof in the case that n is even is incorrect. In fact, there really isn't a proof at all: you just say that it "collapses to the Pythagorean equation" which, needless to say, does not prove its nonexistence.

Your FLT proof in the case that n is odd comes down to the statement that it "should be clear" that the terms have a common factor. This is not clear, and certainly cannot be assumed here!

In conclusion: Your proof of Beal's conjecture uses an incorrect reduction. Your proof of FLT, in both cases, is by asserting something to be true that immediately gives you the truth of the theorem desired. Of course this is unacceptable; you must prove that these are true, not just claim that they are.
CRGreathouse is offline  
December 30th, 2010, 06:31 AM   #4
Global Moderator
 
The Chaz's Avatar
 
Joined: Nov 2009
From: Northwest Arkansas

Posts: 2,766
Thanks: 4

Re: Simple Proof of Fermat's Last Theorem and Beal's Conject

Assume, without loss of generality, that FLT is true.
QED
The Chaz is offline  
December 30th, 2010, 07:35 AM   #5
Newbie
 
Joined: Oct 2009

Posts: 26
Thanks: 0

Re: Simple Proof of Fermat's Last Theorem and Beal's Conject

Quote:
Originally Posted by The Chaz
Assume, without loss of generality, that FLT is true.
QED
You could have saved Andrew W a ton of time if you had just shown him this in the 80s.
UnreasonableSin is offline  
December 30th, 2010, 09:18 AM   #6
Senior Member
 
Joined: Aug 2010

Posts: 158
Thanks: 4

Re: Simple Proof of Fermat's Last Theorem and Beal's Conject

I have dispensed with requiring n to be odd and have attached a slightly revamped proof.
Attached Files
File Type: doc \'s.doc (32.5 KB, 27 views)
MrAwojobi is offline  
December 30th, 2010, 11:12 AM   #7
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Simple Proof of Fermat's Last Theorem and Beal's Conject

Quote:
Originally Posted by MrAwojobi
I have dispensed with requiring n to be odd and have attached a slightly revamped proof.
This fails for exactly the reasons the earlier proof does: it merely asserts that there is a common factor without proving that there is a common factor (let alone finding it) and it transforms the TZ conjecture into a non-integer version of Fermat (which is solvable!).
CRGreathouse is offline  
December 30th, 2010, 11:14 AM   #8
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Simple Proof of Fermat's Last Theorem and Beal's Conject

Would you look over gdmontgomery's FLT proof? I'd really like to know your opinion of it.
http://mymathforum.com/viewtopic.php?f= ... 91&p=70114
CRGreathouse is offline  
December 30th, 2010, 04:07 PM   #9
Senior Member
 
Joined: Aug 2010

Posts: 158
Thanks: 4

Re: Simple Proof of Fermat's Last Theorem and Beal's Conject

Just to give more insight into what I am claiming, ponder this simpler but similar problem. As an example, can (a^3)(b^3) be ever equal to 2(c^3)(d^3), for positive values(and not necessarily integers) of a,b,c and d, if a and b don't share a common factor and c and d don't share a common factor?

The simple answer is 'no' for the reasons outlined in the proof i.e the similarity of structure of the expressions. The different coefficients is simply what would never make them the same given the conditions above.

If you disagree then give a counter example and then I will put this issue to rest.
MrAwojobi is offline  
December 30th, 2010, 08:32 PM   #10
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Simple Proof of Fermat's Last Theorem and Beal's Conject

Did you check that other proof, or at least look it over? I'd really like to know what you think.

Quote:
Originally Posted by MrAwojobi
As an example, can (a^3)(b^3) be ever equal to 2(c^3)(d^3), for positive values(and not necessarily integers) of a,b,c and d, if a and b don't share a common factor and c and d don't share a common factor?
What does "share a common factor" even mean if they're not integers?
CRGreathouse is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
beal, conjecture, fermat, proof, simple, theorem



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Proof Beal's conjecture and Fermat's last theorem HuyThang1981 Number Theory 17 November 21st, 2014 02:57 PM
SIMPLE PROOF OF BEALíS CONJECTURE MrAwojobi Number Theory 106 August 1st, 2014 09:21 PM
Proof Beal's conjecture HuyThang1981 Number Theory 1 January 7th, 2014 08:40 AM
Proof of bealís conjecture akhil verma Number Theory 29 July 21st, 2013 04:51 AM
On The Beal Conjecture And Fermat's Last Theorem. Don Blazys Number Theory 15 April 3rd, 2009 09:04 PM





Copyright © 2018 My Math Forum. All rights reserved.