It all started in 1993, when a banker and mathematical enthusiast named Andrew Beal was investigating generalizations of Fermat’s last theorem. In the middle of the study he came up with an unusual conjecture, with the base of Aˣ + Bʸ = Cᶻ, where A, B, C, x, y, z are positive integers with x, y, z >2, and A, B, and C must have a common prime factor. Sounds complicated? Well, you are not alone, because for over 20 years there has been a prize of one million dollars for those who show proof or present a counterexample.
Mathematics is a wonderful tool, something frustrating for many people, and a true brain-melting machine under the right conditions. Few examples are as blunt as Graham’s number, so large that the universe does not have enough room to write it. Then there are things that we can simply consider beautiful (like the golden ratio), disturbing ( like the doomsday argument), or rare to the core (Galton’s Board).
Now, Beal’s conjecture, formulated in 1993 by the mathematician, banker and poker player Andrew Beal. Like many other mathematicians, Beal decided to cross swords with the historical “Fermat’s Last Theorem,” but through his work he came up with a very similar challenge: Aˣ + Bʸ = Cᶻ, where A, B, C, x, y, z are positive integers with x, y, z > 2, and A, B, and C must have a common prime factor. One of the most cited “solutions” is 3³ + 6³ = 3⁵ with a common factor of 3, and another is 7³ + 7⁴ = 14³, whose common factor is 7.
The conjecture still requires a consolidated and verified test by third parties (the so-called “peer-review”), or as an alternative, a counterexample. In 1997, Beal continued to offer a prize of $5,000 for those who manage to meet one of these goals, until he reached the limit of one million dollars. Today, the reward is in the care of the American Mathematical Society, and as expected, hundreds of enthusiasts on the Web say they have met their requirements. No one has succeeded.
