Everything began in 1993, when a banker and mathematics enthusiast named Andrew Beal was investigating generalizations of Fermat's Last Theorem. While studying it, he came up with a curious conjecture, with the base Aˣ+Bʸ=Cᶻ, where "A, B, C, x, y, z" are positive integers with "x, y, z > 2", and "A, B, C" must have a common prime factor. Sounds complicated? Well, you're not alone, because for over 20 years there has been a million-dollar prize for anyone who proves it completely, or presents 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 compelling as Graham's number, so large that the universe isn't enough to write it down. Then there are things we can simply consider beautiful (say, the golden ratio), disturbing (the doomsday argument), or strange to the core (the Galton board). What do we have here today? Well…
Ladies and gentlemen, the Beal 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 arrived at 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, 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.
https://old.neoteo.com/por-que-277777788888899-es-especial/Now… why is it important? Because of the money! You see, the conjecture still requires a consolidated proof verified by third parties (the so-called "peer-review"), or alternatively, a counterexample. In 1997, Beal decided to offer a prize of $5,000 for anyone who could achieve one of these goals, until he reached the limit of one million dollars. Today, the prize is in the custody of the American Mathematical Society, and as expected, hundreds of enthusiasts on the Web claim to have met its requirements. No one has succeeded...
Source: Fermat's Library on Twitter
Source: Wikipedia
