quadratic reciprocity law

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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

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

• 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 — 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

• 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

• 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

• 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

• Class field theory — In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields. Most of the central results in this area were proved in the period between 1900 and 1950. The theory takes its name… …   Wikipedia

• Carl Friedrich Gauss — Infobox Scientist box width = 300px name = Carl Friedrich Gauss caption = Johann Carl Friedrich Gauss (1777 1855), painted by Christian Albrecht Jensen birth date = birth date|1777|4|30|df=y birth place = Braunschweig, Electorate of Brunswick… …   Wikipedia

• Quaternion algebra — In mathematics, a quaternion algebra over a field, F , is a particular kind of central simple algebra, A , over F , namely such an algebra that has dimension 4, and therefore becomes the 2 times;2 matrix algebra over some field extension of F ,… …   Wikipedia