Beal's conjecture is a conjecture in number theory:
where A, B, C, x, y, and z are positive integers with x, y, z > 2, then A, B, and C have a common prime factor.
Billionaire banker Andrew Beal formulated this conjecture in 1993 while investigating generalizations of Fermat's last theorem. It has been claimed that the same conjecture was independently formulated by Robert Tijdeman and Don Zagier, and it has also been referred to as the Tijdeman-Zagier conjecture.
For a proof or counterexample published in a refereed journal, Beal initially offered a prize of US $5,000 in 1997, raising it to $50,000 over ten years, but has since raised it to US $1,000,000.