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
Famous quotes containing the words refined and/or forms:
“As refined fare serves a hungry man as well as and no better than coarser food, the more pretentious artist will not dream of inviting the hungry man to his meal.”
—Friedrich Nietzsche (1844–1900)
“When we speak the word “life,” it must be understood we are not referring to life as we know it from its surface of fact, but to that fragile, fluctuating center which forms never reach.”
—Antonin Artaud (1896–1948)