# ABC conjecture

The ABC conjecture states that given any $\epsilon>0$, there is a constant $\kappa(\epsilon)$ such that

 $\max(|A|,|B|,|C|)\leq\kappa(\epsilon)(\operatorname{rad}(ABC))^{1+\epsilon}$

for all mutually coprime integers $A$, $B$, $C$ with $A+B=C$, where $\operatorname{rad}$ is the radical of an integer. This conjecture was formulated by Masser and Oesterlé in 1980.

The ABC conjecture is considered one of the most important unsolved problems in number , as many results would follow directly from this conjecture. For example, Fermat’s Last Theorem could be proved (for sufficiently large exponents) with about one page worth of proof.