Abc conjecture

Statement

For every , there exists a constant  such that for any three relatively prime integers  such that:

,

we have the inequality:



where the indicated product is only over prime divisors of the product .

Related facts

Analogous facts over other rings

• Mason-Stothers theorem states that the analogous statement holds over polynomial rings over fields with absolute value replaced by degree -- in fact, we do not even need the .