Mason's theorem is often described as the polynomial case of the (currently unproven) ABC conjecture.
Theorem 1 (Mason-Stothers) Let
be such that
for all , and such that , , and are pair-wise relatively prime. Denote the number of distinct roots of the product by . Then
![$ f(z),g(z),h(z)\in\mathbb{C}[z]$](http://images.planetmath.org:8080/cache/objects/4554/l2h/img1.png "$ f(z),g(z),h(z)\in\mathbb{C}[z]$"){kind=small}
