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Mason-Stothers theorem
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(Theorem)
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Mason's theorem is often described as the polynomial case of the (currently unproven) ABC conjecture.
Theorem 1 (Mason-Stothers) Let $f(z),g(z),h(z)\in\C[z]$ be such that $f(z)+g(z)=h(z)$ for all $z$ , and such that $f$ , $g$ , and $h$ are pair-wise relatively prime. Denote the number of distinct roots of the product $fgh(z)$ by $N$ . Then
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"Mason-Stothers theorem" is owned by mathcam.
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| Other names: |
Mason's Theorem |
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Cross-references: product, roots, number, relatively prime, ABC conjecture, polynomial
This is version 1 of Mason-Stothers theorem, born on 2003-08-05.
Object id is 4554, canonical name is MasonStothersTheorem.
Accessed 4164 times total.
Classification:
| AMS MSC: | 30C15 (Functions of a complex variable :: Geometric function theory :: Zeros of polynomials, rational functions, and other analytic functions ) |
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Pending Errata and Addenda
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