## You are here

HomeMason-Stothers theorem

## Primary tabs

# 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*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff