User:Noosfractal/Beal's Conjecture

While investigating mathematical forms associated with Fermat's last theorem, Andrew Beal noticed a remarkable pattern, leading him to conjecture:


 * Beal's conjecture: if xm + yn = zr, where m, n, r, x, y and z are positive integers with m, n, r > 2, then x, y and z must have a common prime factor.

For example, the solution 33 + 63 = 35 has bases with a common factor of 3, and the solution 76 + 77 = 983 has bases with a common factor of 7. As of 2005, there are no known counterexamples.

A reward of $100,000 is offered for a proof or disproof of the conjecture.