# 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

 $\displaystyle\max\deg\{f,g,h\}+1\leq N.$
Title Mason-Stothers theorem MasonStothersTheorem 2013-03-22 13:49:24 2013-03-22 13:49:24 mathcam (2727) mathcam (2727) 4 mathcam (2727) Theorem msc 30C15 Mason’s Theorem PolynomialAnalogonForFermatsLastTheorem