# Beal conjecture

(Redirected from Beal's conjecture)

The Beal conjecture is the following conjecture in number theory:

Unsolved problem in mathematics:

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

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