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:
“A refined soul is distressed to know that someone owes it thanks; a crude soul, to know that it owes someone thanks.”
—Friedrich Nietzsche (1844–1900)
“Painting dissolves the forms at its command, or tends to; it melts them into color. Drawing, on the other hand, goes about resolving forms, giving edge and essence to things. To see shapes clearly, one outlines them—whether on paper or in the mind. Therefore, Michelangelo, a profoundly cultivated man, called drawing the basis of all knowledge whatsoever.”
—Alexander Eliot (b. 1919)