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Home > Quadratic residue

Otherwise, q is called a quadratic non-residue.

In effect, a quadratic residue modulo p is a number that has a square root in modular arithmetic when the modulus is p. The law of quadratic reciprocity says something about quadratic residues and primes.

Quadratic residues are used in the Legendre symbol. Quadratic reciprocity and the Gauss lemma both reason about quadratic residues.

External links

• MathWorld: Quadratic Residue
• http://primes.utm.edu/glossary/page.php?prev=radix

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Quadratic equationIn mathematics, a quadratic equation is a polynomial equation of the second degree. The generalized form is : The numbers a b and c are called coefficients a is the coefficient of x''2, b is the coefficient of x and c is the free term or constant. Take, f Quadratic reciprocityIn mathematics, the law of quadratic reciprocity in number theory, conjectured by Euler and Legendre and first satisfactorily proved by Gauss, connects the solvability of two related quadratic equations in modular arithmetic. As a consequence, it allows u Quadratic programmingQuadratic programming (QP) is a special type of mathematical optimization problem. The quadratic programming problem can be formulated like this: Assume x belongs to R n space. The (n x n) matrix E is positive semidefinite and h is any (n x 1) vector. Quadratic functionIn mathematics, a quadratic function is a polynomial function of the form :, where a is nonzero. It takes its name from the Latin quadratus for square, because quadratic functions arise in the calculation of areas of squares. In the case where the domain Quadratic residueIn mathematics, a number q is called a quadratic residue modulo p if there exists an integer x such that: : Otherwise, q is called a quadratic non-residue . In effect, a quadratic residue modulo p is a number that has a square root in modular arithmetic w Quadratic formIn mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, the distance between two points in three-dimensional Euclidean space is found by taking the square root of a quadratic form involving six var Quadratic irrational Quadratic field Quadratic integral Quadratic sieve Quadratic residuosity problem