The Beal Prize was funded by Andrew Beal, a prominent banker who is also a mathematics enthusiast. An AMS-appointed committee will award this prize for either a proof of, or a counterexample to, theBeal Conjecture published in a refereed and respected mathematics publication. The prize money – currently US$1,000,000 – is being held in trust by the AMS until it is awarded. Income from the prize fund is used to support the annual Erdős Memorial Lectureand other activities of the Society. The Beal conjecture and prize were announced in an article that appeared in the December 1997 issue of Notices of the American Mathematical Society. One of Andrew Beal’s goals is to inspire young people to think about the equation, think about winning the offered prize, and in the process become more interested in the field of mathematics.
Beal Prize Conjecture
If Ax + By = Cz , where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor.
Procedures for Determination of an Award of the Beal Prize
The administration of the Beal Prize is overseen by a Beal Prize Committee (BPC) to be appointed by the President of the American Mathematical Society (AMS). The formal charge of the BPC and the “Procedures for Determination of an Award of the Beal Prize” are subject to the review and approval by the Council of the AMS.
The Beal Prize Fund is held as a restricted asset of the American Mathematical Society (AMS), with US$1,000,000 to be awarded if, in the judgment of the BPC, the conjecture is proved or a counterexample is presented.
A proposed solution of the Beal Prize Problem may not be submitted directly to the AMS, or to the Beal Prize Committee, or to Mr. Beal. Unpublished manuscripts will not be considered.
The BPC will consider a proposed solution if it is a complete mathematical solution of the Beal Prize Problem. Before consideration, a proposed solution (the “Work”) must be published in a bealprize or by sending mail to:
Beal Prize Committee
c/o Executive Director
American Mathematical Society
201 Charles Street
Providence, RI 02904 USA.
The Work must be widely accepted by the mathematics community following a two-year waiting period after publication. (In the case of a counterexample, that recognition and acceptance by the community may happen much sooner.) Following the waiting period, the BPC will decide whether the Work merits detailed evaluation.
One counter example to Beal's conjecture would be to find positive integers x,m,y,n,z,r such that: x^m + y^n = z^r and m,n,r > 2 and x,y,z co-prime (pairwise no common factor)
For source code and resulting table of tested data which did not find a counterexample using a hash table method, see: