# Beal conjecture

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The Beal conjecture is the following conjecture in number theory:

Unsolved problem in mathematics:

If $A^{x}+B^{y}=C^{z}$ where A, B, C, x, y, z are positive integers and x, y, z are ≥ 3, do A, B, and C have a common prime factor?

If
$A^{x}+B^{y}=C^{z},$ where A, B, C, x, y, and z are positive integers with x, y, z ≥ 3, then A, B, and C have a common prime factor.

Equivalently,

The equation $A^{x}+B^{y}=C^{z}$ has no solutions in positive integers and pairwise coprime integers A, B, C if x, y, z ≥ 3.

The conjecture was formulated in 1993 by Andrew Beal, a banker and amateur mathematician, while investigating generalizations of Fermat's Last Theorem. Since 1997, Beal has offered a monetary prize for a peer-reviewed proof of this conjecture or a counterexample. The value of the prize has increased several times and is currently \$1 million.

In some publications, this conjecture has occasionally been referred to as a generalized Fermat equation, the Mauldin conjecture, and the Tijdeman-Zagier conjecture.