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# Mason-Stothers 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

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

Related:

PolynomialAnalogonForFermatsLastTheorem

Synonym:

Mason's Theorem

Type of Math Object:

Theorem

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

30C15*no label found*

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new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier