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:
“There might be a class of beings, human once, but now to humanity invisible, for whose scrutiny, and for whose refined appreciation of the beautiful, more especially than for our own, had been set in order by God the great landscape-garden of the whole earth.”
—Edgar Allan Poe (18091849)
“The highest perfection of politeness is only a beautiful edifice, built, from the base to the dome, of ungraceful and gilded forms of charitable and unselfish lying.”
—Mark Twain [Samuel Langhorne Clemens] (18351910)