law of quadratic reciprocity

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• Quadratic reciprocity — The law of quadratic reciprocity is a theorem from modular arithmetic, a branch of number theory, which shows a remarkable relationship between the solvability of certain quadratic equations modulo different prime moduli.Although it allows us to… …   Wikipedia

• Proofs of quadratic reciprocity — In the mathematical field of number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusual number of proofs. Several hundred proofs of the law of quadratic reciprocity have been found.Proofs that are …   Wikipedia

• Reciprocity law — may refer to:* Reciprocity law (mathematics), (typefied by the law of quadratic reciprocity) * Reciprocity (photography) …   Wikipedia

• Quadratic residue — In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract… …   Wikipedia

• Quadratic field — In algebraic number theory, a quadratic field is an algebraic number field K of degree two over Q. It is easy to show that the map d ↦ Q(√d) is a bijection from the set of all square free integers d ≠ 0, 1 to the set of… …   Wikipedia

• Reciprocity — may refer to: Reciprocity (Canadian politics) Reciprocity (photography), the relationship between the intensity of the light and duration of the exposure that result in identical exposure Traffic violations reciprocity where non resident drivers… …   Wikipedia

• Reciprocity (mathematics) — In mathematics, reciprocity may mean:* Quadratic reciprocity, a fundamental result in number theory. Generalisations include: **cubic reciprocity **biquadratic reciprocity **higher reciprocity laws **Artin reciprocity **Weil reciprocity for… …   Wikipedia

• Artin reciprocity law — The Artin reciprocity law, established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of the global class field theory.[1] The term reciprocity law refers to a long line of… …   Wikipedia

• Legendre symbol — The Legendre symbol or quadratic character is a function introduced by Adrien Marie Legendre in 1798 [A. M. Legendre Essai sur la theorie des nombres Paris 1798, p 186] during his partly successful attempt to prove the law of quadratic… …   Wikipedia

• Number theory — A Lehmer sieve an analog computer once used for finding primes and solving simple diophantine equations. Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers (the… …   Wikipedia

• mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium