# Beal’s Conjecture

Beal’s Conjecture – a generalized Fermat’s Last Theorem.

Banker Andrew Beal offers \$1m for maths solution.

BEAL’S CONJECTURE:
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.

## 3 thoughts on “Beal’s Conjecture”

1. This is an excellent post on Beal’s Conjecture.

2. I have a really stupid question.

Based on the criteria:
If
A^{x} + B^{y} = C^{z}
A) where A, B, C, x, y and z are positive integers and
B) x, y and z are all greater than 2,
then A, B and C must have a common prime factor.

Why can’t it just be disproved as such:
2^3 + 2^3 ≠ 2^3
(or any combination where A=B=C && x=y=z)
?
Clearly, it can’t be that simple, but what criteria am I missing? Is it just implied that well duh, you can’t have A=B=C AND x=y=z ?

In your examples, it’s okay to have A=B=C,
and for x=y, and y=z
but not x=y=z.

Wait …
that has to do with Fermat’s Theorem being proven that
A^n + B^n ≠ C^n for integers greater than 2.
Never mind.

It’s late. I haven’t studied math since high school.

• It is a million dollar question…