Billionaire banker Andrew Beal formulated Beal's Conjecture in 1993 while investigating generalizations of Fermat's Last Theorem. The conjecture states: "If A^x + B^y = C^z, where A, B, C, x, y, and z are positive integers with x, y, z > 2, then A, B, and C have a common prime factor." For example, the solution 3^3 + 6^3 = 3^5 has bases with a common factor of 3, and 7^6 + 7^7 = 98^3 has bases with a common factor of 7. Beal's Conjecture has been compared to other conjectures in number theory, including Fermat's Last Theorem and the Fermat-Catalan Conjecture.
For a proof or counterexample published in a refereed journal, Beal initially offered a prize of 5,000 USD in 1997, raising it to 50,000 USD over ten years, but has since raised it to US $1,000,000. Think you can come up with anything? For more info, go to http://en.wikipedia.org/wiki/Beal%27s_conjecture. For info on Fermat's Last Theorem, as well as the Fermat-Catalan Conjecture, please refer to the following sites: