abc conjecture

== English == === Alternative forms === abc-conjecture ABC conjecture === Etymology === From the names of the variables a, b, and c. The conjecture was proposed in 1985. === Noun === abc conjecture (plural abc conjectures) (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. Any of certain generalisations of the conjecture. ==== Synonyms ==== (conjecture in number theory): Oesterlé-Masser conjecture ==== Translations ==== === Further reading === Radical of an integer on Wikipedia.Wikipedia