· Google ·
Posted on 03/10/2009 5:28:15 PM PDT by SunkenCiv
No one suspected that Ax + By = Cz (note unique exponents) might also be impossible with co-prime bases until a remarkable discovery in 1993 by a Dallas, Texas number theory enthusiast by the name of Andrew Beal. Beal was working on FLT when he began to look at similar equations with independent exponents. He constructed several algorithms to generate solution sets but the very nature of the algorithms he was able to construct required a common factor in the bases. He began to suspect that co-prime bases might be impossible and set out to test his hypothesis by computer. Beal and a colleague programmed 15 computers and after thousands of cumulative hours of operation had checked all variable values through 99. Many solutions were found: all had a common factor in the bases. While certainly not conclusive, Beal now had sufficient reason to share his discovery with the world.
BEAL'S CONJECTURE: If Ax + By = Cz, where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor.
(Excerpt) Read more at math.unt.edu ...
“Asking NASA to develop low cost space access is analogous to asking Amtrak to develop new low cost locomotives or the US Postal Service to develop new low cost electronic mail systems.” — Andrew Beal
Beal Aerospace (R.I.P., a well done)
various | 1997 through present | various
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http://www.freerepublic.com/focus/f-bloggers/1781167/posts
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· Google ·
Wonderful.
But, what does the answer mean?
nice to see something like this posted here.
um.... huh?
Beal’s Conjecture Disproved
James Constant
Beal’s Conjecture is disproved for the same reasons Fermat’s Last Theorem is proved.
[I’m not too bright, but it appears to me that JC doesn’t understand the Beal Conjecture]
http://www.coolissues.com/mathematics/Beal/beal.htm
Last-Digit Terminations and the Beal Conjecture: An Explanation
by Charles William Johnson
http://www.earthmatrix.com/beal/conjecture.htm
Beal’s Conjecture: A Search for Counterexamples
http://norvig.com/beal.html
Ooops.
The conjecture is not valid over the larger domain of Gaussian integers. After a prize of $50 was offered for a counterexample, Fred W. Helenius provided (-2 + i)3 + (-2 - i)3 = (1 + i)4. *
what you said. ;’)
Thanks, it’s a pleasure. For some reason I started thinking about Beal’s Conjecture today at work, and used a golden opportunity to expand my personal frontiers of knowledge (i.e., surf the web on work time) to find out what its status is.
I tried reading a couple of little books on the proof of FLT (as opposed to FTL ;’) and while found the efforts of the guy who pulled it off to be inspirational, I had no clue what was going on.
Okay, now, for something comp-, well, you know...
Digital Blasphemy, my favorite online digital art site, has some very nice freebies, most of them appear to be pretty new:
http://www.digitalblasphemy.com/freegallery.shtml
Cheers!
what you said. ;’)
Uh, yeah, I think.
Cheers!
As could almost anyone who put their mind to it. Beal's conjecture definitely falls into that category for me. A complete waste of time. Beal is not even a mathematician, just a billionaire math enthusiast who's come up with his little conjecture and thrown $100,000 at it to reel in some poor fish. It hurts mathematics more than helps it, imo, as it will undoubtedly divert mathematicians from more important work.
C'mon, Andy, you're a bazillionaire, for crying out loud. What is the solution to you? Why are you interested? Does it make you feel smart and important because you came up with a problem that mathematicians can't solve? Even though a monkey could do the same thing? Listen, it could take an entire lifetime to prove or disprove your conjecture. Make it worth our while, say $10,000,000? Even ten million dollars for all the lives wasted isn't much!
Shows what Gauss knew. The proof of FLT resulted in breakthroughs in two (admittedly arcane) areas of mathematics, and also pointed to the generally accepted fact that Fermat’s unelaborated “remarkable proof” must have been one of the false ones rediscovered between his time and the late 1990s.
But anyway, don’t hold back! Let us know how you really feel! ;’)
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