abc conjecture

Alternative forms

 * abc-conjecture

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

Noun

 * 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).
 * 2) * 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.
 * 1) Any of certain generalisations of the conjecture.
 * 1) Any of certain generalisations of the conjecture.
 * 1) Any of certain generalisations of the conjecture.
 * 1) Any of certain generalisations of the conjecture.

Translations

 * French: conjecture abc
 * German: abc-Vermutung
 * Italian: congettura abc
 * Portuguese: conjetura abc
 * Spanish: conjetura abc