Abc conjecture

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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 .

Weaker facts and conjectures