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Beal Prize

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, the Beal 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 Lecture and 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 A^{x} + B^{y} = C^{z} , 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.

[By way of example, 3^{3} + 6^{3} = 3^{5}, but the numbers that are the bases have a common factor of 3, so the equation does not disprove the theorem; it is not a counterexample.]

**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 Unpublished manuscripts will not be considered.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 refereed mathematics publication which is respected and, in the opinion of the BPC, maintains the highest editorial standards (or published in another form as the BPC decides may qualify). In the case of a counterexample, the proposed solution will be subject to independent verification. Upon publication, the author(s) of the Work should notify the AMS and the BPC by sending email to bealprize@ams.org 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.

If the Work is to receive detailed evaluation, the BPC and the AMS will identify at least two experts who can verify the correctness of the Work and who are not members of the BPC to assist in the evaluation. Upon completion of the evaluation, if the BPC can make a clear decision, it may award the prize and determine attribution of credit for a solution. The BPC will consider whether a solution relies directly on contributions of others published prior to the Work and it may divide the prize among multiple contributors.

If upon completion of the evaluation the BPC cannot make a clear decision, the BPC may decide that no award should be made at that time. The BPC may revisit a decision to make no award if new information becomes available. All deliberations of the BPC or of experts assisting in an evaluation are confidential.