Frank Vega
Abstract
It was proved if $A^{x} + B^{y} = C^{z}$, 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. Therefore, it was demonstrated the Beal's conjecture as a consequence of using a modification to the Binomial theorem.
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
It was proved if $A^{x} + B^{y} = C^{z}$, 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. Therefore, it was demonstrated the Beal's conjecture as a consequence of using a modification to the Binomial theorem.
Key concepts: Number theory, Beal's conjecture, Mathematics, Conjecture, Binomial theorem, Prime (order theory), Combinatorics, Discrete mathematics