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Mason-Stothers theorem (Theorem)

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\mathbb{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
$\displaystyle \max\deg\{f,g,h\}+1\leq N.$    



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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 2992 times total.

Classification:
AMS MSC30C15 (Functions of a complex variable :: Geometric function theory :: Zeros of polynomials, rational functions, and other analytic functions )

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