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quadratic reciprocity

quadratic reciprocity noun: the mathematical theorem which states that, for given odd prime numbers p and q, the question of whether p is a square modulo q is equivalent to the question of whether q is a square modulo p.

Noun

quadratic reciprocity (uncountable)

  1. The mathematical theorem which states that, for given odd prime numbers p and q, the question of whether p is a square modulo q is equivalent to the question of whether q is a square modulo p.
    • Yes, but we need not only Quadratic Reciprocity but also Dirichlet's theorem on primes in arithmetic progressions to see this.2007, Paul B. Garrett, Abstract Algebra, Taylor & Francis (Chapman Hall/CRC Press), page 287
    • Gauss studied these sorts of numbers while attempting to formulate and prove higher order reciprocity laws, following his success with quadratic reciprocity.2009, Sam Vandervelde, Circle in a Box, American Mathematical Society, page 153

Forms of quadratic reciprocity

alternative formlaw of quadratic reciprocity

Origin of quadratic reciprocity

The theorem highlights a particular form of reciprocity in the solvability of the quadratic equation a² = b in modular arithmetic. It was conjectured by Leonhard Euler and Adrien-Marie Legendre and first proved by Carl Friedrich Gauss.

Questions about quadratic reciprocity

What does quadratic reciprocity mean?
Quadratic reciprocity means the mathematical theorem which states that, for given odd prime numbers p and q, the question of whether p is a square modulo q is equivalent to the question of whether q is a square modulo p.
What part of speech is quadratic reciprocity?
Quadratic reciprocity is a noun.

Words near quadratic reciprocity in the dictionary

  1. quadratic functions
  2. quadratic integer
  3. quadratic integers
  4. quadratic mean
  5. quadratic means
  6. quadratic reciprocity
  7. quadratic residue
  8. quadratic residues
  9. quadratic surd
  10. quadratic surds
  11. quadratic time

Source and license

Adapted from Wiktionary: quadratic reciprocity (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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