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Jacobi symbol

Jacobi symbol noun: a mathematical function of integer a and odd positive integer b, generally written (a/b), based on, for each of the prime factors pᵢ of b, whether a is a quadratic residue or nonresidue modulo pᵢ.

Noun

Jacobi symbol (plural Jacobi symbols)

  1. A mathematical function of integer a and odd positive integer b, generally written (a/b), based on, for each of the prime factors pᵢ of b, whether a is a quadratic residue or nonresidue modulo pᵢ.
    • Although the Jacobi symbol ((1009)/(2307))=1, we still cannot determine whether or not the quadratic congruence 1009=x²(mod 2307) is soluble.
      Remark 1.6.10. Jacobi symbols can be used to facilitate the calculation of Legendre symbols.2000, Song Y. Yan, Number Theory for Computing, Springer, 2000, Softcover reprint, page 114
    • With more than two factors, having a Jacobi symbol of 1 only means that x may be a quadratic non-residue modulo an even number of factors only. Thus in the general case, the Jacobi symbol is not enough to test for the existence of a discrete logarithm. Thanks to this efficient test, given any...2009, Antoine Joux, “Chapter 1: Introduction to Identity-Based Cryptography”, in Marc Joye, Gregory Neven, editors, Identity-based Cryptography, IOS Press, page 8

Forms of Jacobi symbol

pluralJacobi symbols

Origin of Jacobi symbol

Named after German mathematician Carl Gustav Jakob Jacobi, who introduced the notation in 1837.

Questions about Jacobi symbol

What does Jacobi symbol mean?
Jacobi symbol means a mathematical function of integer a and odd positive integer b, generally written (a/b), based on, for each of the prime factors pᵢ of b, whether a is a quadratic residue or nonresidue modulo pᵢ.
What part of speech is Jacobi symbol?
Jacobi symbol is a noun.
What is the plural of Jacobi symbol?
The plural of Jacobi symbol is Jacobi symbols.

Words near Jacobi symbol in the dictionary

  1. Jacobi ellipsoids
  2. Jacobi identities
  3. Jacobi identity
  4. Jacobi polynomial
  5. Jacobi polynomials
  6. Jacobi symbol
  7. Jacobi symbols
  8. jacobian
  9. Jacobian conjecture
  10. Jacobian conjectures
  11. jacobians

Source and license

Adapted from Wiktionary: Jacobi symbol (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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