Refined Forms and Generalizations
A stronger inequality proposed by Baker (1998) states that in the inequality, one can replace rad(abc) by
- ε−ωrad(abc)
where ω is the total number of distinct primes dividing a, b and c (Bombieri & Gubler 2006, p. 404). A related conjecture of Andrew Granville states that on the RHS we could also put
- O(rad(abc) Θ(rad(abc)))
where Θ(n) is the number of integers up to n divisible only by primes dividing n.
Browkin & Brzeziński (1994) formulated the n-conjecture—a version of the abc conjecture involving integers.
Read more about this topic: abc Conjecture
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