05.24.07

Beal’s Conjecture

Posted in math, programming at 9:47 pm by danvk

(I noticed today that Rice has finally taken down my owlnet page. Over the next few weeks, I’ll be giving some of the interesting pages from that site a new home here on danvk.org. First up is Beal’s Conjecture…)

I’ve put a link to last summer’s work on Beal’s Conjecture over on the right-hand side of the site. A quick overview:

Beal’s conjecture states that, if (x,y,z) are co-prime and m,n,r ≥ 3, then x^m + yⁿ ≠ z^r. Sound familiar? It should. It’s a generalization of Fermat’s Last Theorem.

What makes Beal’s conjecture especially exciting is that Andrew Beal, a Texas billionaire, has put a $100,000 prize on the proof or disproof of the problem. If it’s false (and most generalizations of FLT have been), then a computer search may have a chance of coming up with the counterexample. Peter Norvig did an initial hunt but came up empty. I extended his results, and also came up empty. Now that I have access to lots of machines, I’d like to extend the search a bit further.

The old article I wrote is still valid, though it contains a misstatement that’s made all the more embarrassing by being in ALL CAPS. I’ll be lazy and leave it as one of those pesky “exercises to the reader” to figure out how I goofed.

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