Mason-Stothers theorem
MasonStothersTheorem
2003-08-05 18:01:46
2003-08-05 18:01:46
Theorem
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Mason's theorem is often described as the polynomial case of the (currently unproven) ABC conjecture.
\begin{Theo}[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
\begin{align*}
\max\deg\{f,g,h\}+1\leq N.
\end{align*}
\end{Theo}