Word.ws English Dictionary

abc conjecture

abc conjecture 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

abc conjecture (plural abc conjectures)

  1. 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).
    • 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.1985, Paul Vojta, Appendix, Serge Lang, Introduction to Arakelov Theory, Springer, 1988 Softcover, page 156
    • The abc conjecture may well replace the Fermat theorem for the future generation of mathematicians.2004, Sergei K. Lando, R.V. Gamkrelidze, V.A. Vassiliev, Graphs on Surfaces and Their Applications, Springer, page 137
  2. Any of certain generalisations of the conjecture.

Synonyms of abc conjecture

Forms of abc conjecture

pluralabc conjectures
alternative formabc-conjecture
alternative formABC conjecture

Origin of abc conjecture

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

Questions about abc conjecture

What does abc conjecture mean?
Abc conjecture means 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).
What part of speech is abc conjecture?
Abc conjecture is a noun.
What is the plural of abc conjecture?
The plural of abc conjecture is abc conjectures.

Words near abc conjecture in the dictionary

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  2. ABC
  3. ABC art
  4. ABC book
  5. ABC books
  6. abc conjecture
  7. ABC guide
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  9. ABC island
  10. ABC Islands
  11. ABC parties

Source and license

Adapted from Wiktionary: abc conjecture (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “abc conjecture.” Word.ws, https://word.ws/abc_conjecture. Based on Wiktionary, CC BY-SA 4.0.