Beal’s Conjecture


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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.

http://metro.co.uk/2013/06/05/texas-banker-offering-1m-for-answer-to-30-year-old-maths-problem-3829105/

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3 thoughts on “Beal’s Conjecture

  1. 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.

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