Meaning of abc conjecture | Babel Free
Definitions
- 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).
- Any of certain generalisations of the conjecture.
Equivalents
Deutsch
abc-Vermutung
Español
conjetura abc
Français
conjecture abc
Italiano
congettura abc
Português
conjetura abc
Examples
“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.”
CEFR level
B2
Upper Intermediate
This word is part of the CEFR B2 vocabulary — upper intermediate level.
This word is part of the CEFR B2 vocabulary — upper intermediate level.