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Legendre symbol

Legendre symbol noun: a mathematical function of an integer and a prime number, written (a/p), which indicates whether a is a quadratic residue modulo p.

Noun

Legendre symbol (plural Legendre symbols)

  1. A mathematical function of an integer and a prime number, written (a/p), which indicates whether a is a quadratic residue modulo p.
    • Our only method at present for the computation of Legendre symbols requires a possible consideration of (p-1)/2 congruences (unless, of course, we are fortunate enough to encounter the desired quadratic residue along the way).1994, James K. Strayer, Elementary Number Theory, Waveland Press, 2002, Reissue, page 109
    • The Jacobi symbol, which generalizes the Legendre symbol, sheds some additional light on how to determine whether (7.29) has solutions when m has two or more distinct prime factors.2006, Neville Robbins, Beginning Number Theory, 2nd edition, Jones & Bartlett, page 195

Forms of Legendre symbol

pluralLegendre symbols

Origin of Legendre symbol

Named after French mathematician Adrien-Marie Legendre (1752–1833), who introduced the symbol in 1798 in his work Essai sur la Théorie des Nombres ("Essay on the Theory of Numbers").

Questions about Legendre symbol

What does Legendre symbol mean?
Legendre symbol means a mathematical function of an integer and a prime number, written (a/p), which indicates whether a is a quadratic residue modulo p.
What part of speech is Legendre symbol?
Legendre symbol is a noun.
What is the plural of Legendre symbol?
The plural of Legendre symbol is Legendre symbols.

Words near Legendre symbol in the dictionary

  1. Legendre
  2. Legendre form
  3. Legendre forms
  4. Legendre polynomial
  5. Legendre polynomials
  6. Legendre symbol
  7. Legendre symbols
  8. Legendre transformation
  9. Legendre transformations
  10. Legendre's conjecture
  11. Legendre's constant

Source and license

Adapted from Wiktionary: Legendre 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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