Banker Offers $1M To Solve Beal Conjecture 216
oxide7 writes "A Texas banker with a knack for numbers has offered $1 million for anyone who can solve a complex math equation that has stumped mathematicians since the 1980s. The Beal Conjecture states that the only solutions to the equation A^x + B^y = C^z, when A, B and C are positive integers, and x, y and z are positive integers greater than two, are those in which A, B and C have a common factor. Like most number theories, it's "easy to say but extremely difficult to prove.""
What's in it for him? (Score:3, Insightful)
So, being quite cynical about such things, in what way would a proof of this conjecture allow him to make more money?
Philanthropy and advancing science are good, but my first thoughts is that if someone can prove this he stands to make massive amounts of money.
or maybe (Score:2, Insightful)
Why don't they just put up a simple problem and pay out $1 each for up to 1 million students who can solve it.
Re:Couldn't you just make up any old equation... (Score:5, Insightful)
Only if x=y=z. For instance, somebody above suggested 3^3 + 6^3 = 3^5 (27+216=243). If we factor out the common 3, we get 3^2 + 2*(6^2) = 3^4 (9+72=81), which no longer has the right form because 72 is not a power of any number.
If x=y=z, and if A^x+B^x=C^x where A,B,C had the same greatest common factor n, then you could divide all three numbers by n^x and get a new formula (A/n)^x+(B/n)^y=(C/n)^z where A/n, B/n, and C/n had no common factor, and if Beal's conjecture is true then these numbers cannot exist if x>2. Therefore A^x+B^x=C^x has no nontrivial solution for x>2, which is Fermat's last theorem.