abc conjecture

Hello, you have come here looking for the meaning of the word abc conjecture. In DICTIOUS you will not only get to know all the dictionary meanings for the word abc conjecture, but we will also tell you about its etymology, its characteristics and you will know how to say abc conjecture in singular and plural. Everything you need to know about the word abc conjecture you have here. The definition of the word abc conjecture will help you to be more precise and correct when speaking or writing your texts. Knowing the definition ofabc conjecture, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.

English

English Wikipedia has an article on:
Wikipedia

Alternative forms

Etymology

From the names of the variables a, b, and c. The conjecture was proposed in 1985.

Noun

abc conjecture (plural abc conjectures)

  1. (number theory) 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).
    • 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.
    • 2004, Sergei K. Lando, R.V. Gamkrelidze, V.A. Vassiliev, Graphs on Surfaces and Their Applications, Springer, page 137:
      The abc conjecture may well replace the Fermat theorem for the future generation of mathematicians.
    • 2006, Pei-Chu Hu, Chung-Chun Yang, Value Distribution Theory Related to Number Theory, Springer (Birkhäuser), page 233:
      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.
    • 2007, Enrico Bombieri, Walter Gubler, Heights in Diophantine Geometry, Cambridge University Press, page 401:
      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.
  2. Any of certain generalisations of the conjecture.

Synonyms

Translations

Further reading

Wikious
Boobota
Sagapedia