abc conjecture

名词 n.
中文释义

英文释义

名词 n.
  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).
    — 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.
  2. Any of certain generalisations of the conjecture.

词形变化

abc conjectures plural abc-conjecture alternative ABC conjecture alternative

词源

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