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.
Source : bealconjecture.com
The conjecture was proposed in 1993 by self-taught mathematician Andrew Beal, who was working on aspects of Fermat's Last Theorem.
The American Mathematical Society is holding in trust a $1,000,000 prize fund for anyone who can prove (or disprove) the conjecture.