abc conjecture
Word Rarity
Rare
Frequency: 3.30 in modern English
28
Scrabble Score
13
Letters
4
Syllables
10
Unique Chars
Meaning
noun
Given coprime positive integers a, b and c, such that a + b = c, and d the radical of abc (the product of its distinct prime factors), the conjecture that d is usually not much smaller than c (in other words, that if a and b are divisible by large powers of primes, then c usually is not).
noun
Any of certain generalisations of the conjecture.
Example Sentences
- "1985, Paul Vojta, Appendix, Serge Lang, Introduction to Arakelov Theory, Springer, 1988 Softcover, page 156, Finally in §5 we give one application to the curve X⁴ + Y⁴ = Z⁴, showing that the height inequalities for the curve imply the asymptotic Fermat conjecture and a weak form of the Masser-Oesterlé abc''' conjecture."
- "The abc''' conjecture may well replace the Fermat theorem for the future generation of mathematicians."
- "To prove or disprove the abc'''-conjecture would be an important contribution to number theory.[…]Langevin ([236], [237]) proved that the abc'''-conjecture implies the Erdős-Woods conjecture with k = 3 except perhaps a finite number of counter examples."
- "The abc'''-conjecture of Masser and Oesterle is a typical example of a simple statement that can be used to unify and motivate many results in number theory, which otherwise would be scattered statements without a common link."
Etymology
Inflected Forms
abc conjectures (plural)
abc-conjecture (alternative)