Last Updated：2025/11/30

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(mathematics) A conjecture stating that, if Aˣ+Bʸ=Cᶻ, where A, B, C, x, y, and z are positive integers with x, y, z > 2, then A, B, and C have a common prime factor.

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Beal's conjecture

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Source Word

Beal's conjecture

Proper noun

(mathematics) A conjecture stating that, if Aˣ+Bʸ=Cᶻ, where A, B, C, x, y, and z are positive integers with x, y, z > 2, then A, B, and C have a common prime factor.

Japanese Meaning

Bealの予想（またはBealの公準）: 正の整数 A, B, C, x, y, z（ただし x, y, z > 2）があり、もし A^x + B^y = C^z が成り立つならば、A, B, C は共通の素因数を持つという数学の予想

What is this buttons?

Beal's conjecture has driven many mathematicians to search for either a proof or a counterexample to the equation A^x + B^y = C^z under the condition that x, y, and z are greater than 2.

Google Translation / DeepL Translation

A、B、C、x、y、z が正の整数で x、y、z > 2 の場合に A^x + B^y = C^z ならば A、B、C は共通の素因数を持つとする予想は、その方程式の証明や反例を求める多くの数学者の探究を促してきた。

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(mathematics) A conjecture stating that, if Aˣ+Bʸ=Cᶻ, where A, B, C, x, y, and z are positive integers with x, y, z > 2, then A, B, and C have a common prime factor.

Details

Beal's conjecture

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