Beal's conjecture

We prove if $A^{x} + B^{y} = C^{z}$, where $A$, $B$, $C$, $x$, $y$ and $z$ are positive integers, $x$, $y$ and $z$ are all greater than $2$, then $A$, $B$ and $C$ must have a common prime factor. In this way, we demonstrate the Beal's conjecture using the properties of divisibility and applying the reductio ad absurdum.