Mathematicians have long been intrigued by Pierre Fermat's famous assertion that A^x + B^x = C^x is impossible (as stipulated) and the remark written in the margin of his book that he had a demonstration or "proof". This became known as Fermat's Last Theorem (FLT) despite the lack of a proof. Andrew Wiles proved the relationship in 1994, though everyone agrees that Fermat's proof could not possibly have been the proof discovered by Wiles. Number theorists remain divided when speculating over whether or not Fermat actually had a proof, or whether he was mistaken. This mystery remains unanswered though the prevailing wisdom is that Fermat was mistaken. This conclusion is based on the fact that thousands of mathematicians have cumulatively spent many millions of hours over the past 350 years searching unsuccessfully for such a proof.

It is easy to see that if A^x + B^x = C^x then either A, B, and C are co-prime or, if not co-prime that any common factor could be divided out of each term until the equation existed with co-prime bases. (Co-prime is synonymous with pairwise relatively prime and means that in a given set of numbers, no two of the numbers share a common factor.)

You could then restate FLT by saying that A^x + B^x = C^x is impossible with co-prime bases. (Yes, it is also impossible without co-prime bases, but non co-prime bases can only exist as a consequence of co-prime bases.)

Three mathematicians by the names of Andrew Granville, Alf Vanderpoorten, and Andrew Bremmer set out to discredit and criticize Andy Beal and the attribution of the conjecture, including writing scathing criticisms claiming that the conjecture was previously known and evidenced in prior works dating back to Brun's work of 1914.  The untruthfulness and motivations of their criticisms were made obvious by the subsequent 1996 publication of Vanderpoorten's book wherein he claims to propose the conjecture as recent original thought by none other than …. himself (see page 194 of Vanderpoorten's "notes on Fermat's Last Theorem," 1st edition).  Equally interesting, the Beal conjecture has more recently (after 2010, almost 20 years after Beal's dissemination of the conjecture) also been incorrectly referred to as the Tijdeman-Zagier conjecture, although no known evidence exists as to when or where Tijdeman or Zagier ever conjectured or disseminated any such conjecture. Apparently Vanderpoorten himself also would contest the Tijdeman-Zagier attribution as evidenced by his 1996 publication referenced above. The fact remains that while many people may claim they made the discovery, no evidence has ever been produced predating Beal's discovery and widespread dissemination of the conjecture in 1993.

By offering a cash prize for the proof or disproof of this important number theory relationship, Andy Beal hopes to inspire young minds to think about the equation, think about winning the offered prize, and in the process become more interested in the wonderful study of mathematics. Information regarding the $1,000,000 cash prize that is held in trust by the American Mathematics Society can be obtained http://www.math.unt.edu/~mauldin/beal.html or https://www.ams.org/profession/prizes-awards/ams-supported/beal-prize-rules.