February 20th, 2014, 10:06 AM  #1 
Senior Member Joined: Aug 2010 Posts: 158 Thanks: 4  Beal's Conjecture Conjecture
I conjecture that all examples of the Beal Conjecture equation A^x + B^x = C^z where A,B.C.x,y,z are positive integers and x>2, y>2, z>2 can be transformed to a Beal Conjecture equation of 5 variables and not 6 i.e. 2 of the 3 powers x,y or z will be the same. Can anyone supply the proof or a counterexample ?

February 20th, 2014, 10:14 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Beal's Conjecture Conjecture
If I understand you correctly, you're saying that if x, y, and z are distinct integers greater than 2 then there are no positive integers A, B, and C such that A^x + B^y = C^z. Is that right?

February 20th, 2014, 10:26 AM  #3 
Senior Member Joined: Aug 2010 Posts: 158 Thanks: 4  Re: Beal's Conjecture Conjecture
What you are saying is not what I am saying. I am simply conjecturing that all the Beal equation examples can be rewritten such that 2 powers out of 3 will be the same.

February 20th, 2014, 11:51 AM  #4  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Beal's Conjecture Conjecture Quote:
I constructed it using as a seed, This just barely misses Beal criteria, exponent 2 is not allowed. Last edited by skipjack; May 9th, 2014 at 03:41 AM.  
February 20th, 2014, 12:08 PM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Beal's Conjecture Conjecture Quote:
 
February 20th, 2014, 12:21 PM  #6 
Senior Member Joined: Aug 2010 Posts: 158 Thanks: 4  Re: Beal's Conjecture Conjecture
agentredium, you have not disappointed me because as you yourself acknowledge, your example simplifies to an equation that doesn't fulfil the Beal condition. CRGreathouse what I am conjecturing is that every example of the Beal equation will always be manipulated to give another Beal equation via multiplication, division or rewriting a P^Q = R^S such that eventually 2 of the powers will be the same.

February 20th, 2014, 12:47 PM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Beal's Conjecture Conjecture
I'm just trying to find out what you mean by Quote:
 
February 20th, 2014, 01:13 PM  #8  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Beal's Conjecture Conjecture Quote:
Take Where it 'seems' like the three exponents are all different but it is easy to manipulate this to These are the SAME number (2^9) and two out of three exponents are equal. Note that both representations above of 2^9 satisfy the Beal criteria but you cannot manipulate and get the same number (700000^3) with two out of three exponents equal. My counterexample satisfies the Beal criteria for the bases and exponents and there is a common factor of so it is NOT a counterexample to Beal. It is a counterexample to your claim however, IFF I understand your claim correctly. If you do not require that the number be kept the same after the transformation, then your conjecture is true. Last edited by skipjack; May 9th, 2014 at 03:43 AM.  
February 20th, 2014, 02:01 PM  #9 
Senior Member Joined: Aug 2010 Posts: 158 Thanks: 4  Re: Beal's Conjecture Conjecture
agentredium your last statement is correct. It seems you now agree with my conjecture. Can you prove it? CRGreathouse I think agentredium has provided a good explanation of what I am on about.

February 20th, 2014, 02:36 PM  #10 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Beal's Conjecture Conjecture
agent, if you do understand this, would you translate please?


Tags 
beal, conjecture 
Search tags for this page 
beal conjecture examples,beal conjecture pdf,counterexample to beal's conjecture,counterexample to beal,beal conjecture formulas,beals conjecture,Beal's conjecture special exponents
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Beal's Conjecture  bigbuck  Number Theory  20  August 2nd, 2014 05:01 AM 
SIMPLE PROOF OF BEAL’S 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 
I Reject the Beal Conjecture  ducnhuandoan  Number Theory  68  December 22nd, 2013 11:37 PM 
Proof of beal’s conjecture  akhil verma  Number Theory  29  July 21st, 2013 04:51 AM 