The field of mathematics is abundant in its wide array of unsolved problems and assertions that remain to be proved or disproved. A proposed theorem which has not yet been proved is known as a conjecture.
The Beal Conjecture – An Offshoot of Fermat’s Last Theorem
Andrew Beal is a Dallas-based businessman who is also a number theory enthusiast. He was working on Fermat’s Last Theorem in 1993 when he began to explore similar equations. Fermat’s Last Theorem, of course, states that there do not exist non-zero integers a, b and c, and an integral exponent x > 2 such that a ^ x + b ^ x = c ^ x.
Beal explored the possibility of modifying the equation by introducing unique exponents. The Beal Conjecture states that 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.
Beal wrote to many experts in the field of number theory and to mathematical journals. Among the first to acknowledge his discovery were Dr. Harold M. Edwards from the department of mathematics at New York University and author of Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Springer, 1996), and Jarell Tunnell, who was referred by Dr. Earl Taft from the department of mathematics at Rutgers University. They acknowledged that the conjecture had been previously unknown to the mathematical world.
On a side note, Fermat's Last Theorem was known as a theorem, not a conjecture, even when it existed without a proof.
Finding a Proof (or Disproof) of the Beal Conjecture
Andrew Beal offers a 100,000 dollar prize for the first person to find a proof or a counter example to the Beal problem. The prize money is held by the American Mathematical Society. A panel has been appointed to verify the correctness and accuracy of proofs or counter examples proposed by mathematicians and students.
The panel includes Professor R. Daniel Mauldin from the University of North Texas, along with Charles Fefferman and Ron Graham. Information on the prize and relevant contact details are available on the University’s website.
Attempts have been made to find counter examples using computer programs, but they have failed to yield any results so far.
Beal hopes that the prize money offered will encourage fresh, young minds to attempt to formulate a proof for his conjecture. Sixteen years after its discovery, The Beal Conjecture remains an unsolved mystery in the field of number theory.
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