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## Beal's conjecture

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posted on 02.04.2018 by Frank Vega#### online resource

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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.