- quadratic reciprocity
- мат. квадратичная взаимность
Большой англо-русский и русско-английский словарь. 2001.
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
quadratic reciprocity — noun Mathematical theorem relating the Jacobi symbol to the inverted , essentially relating the question of whether a is a square modulo b to the opposite question of whether b is a square modulo a (or modulo the prime factors) … Wiktionary
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
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 — In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms. Quadratus is Latin for square . Mathematics Algebra… … 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 (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 — 1. adjective a) square shaped b) of a polynomial, involving the second power (square) of a variable but no higher powers, as . 2. noun A quadratic polynomial, function or equation. See Also: quadrate, quadratic equation, quadratic fo … Wiktionary
Quadratic Gauss sum — For the general type of Gauss sums see Gaussian period, Gauss sumIn mathematics, quadratic Gauss sums are certain sums over exponential functions with quadratic argument. They are named after Carl Friedrich Gauss, who studied them… … Wikipedia
