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ετυμολογία

Τι (ποιος) είναι quadratic residue generator - ορισμός

IN NUMBER THEORY CONCERNING PRIMES

Euler criterion; Euler's quadratic residue theorem; Euler quadratic residue theorem; Euler's Criterion

Quadratic residue

INTEGER THAT IS A PERFECT SQUARE MODULO SOME INTEGER

Quadratic residues; Quadratic non-residue; Quadratic congruences; Quadratic congruence; Modular square root; Square root modulo n; Square root mod n; Quadratic residuosity; Quadratic nonresidue; Least quadratic non-residue; Quadratic excess

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.

https://en.wikipedia.org/wiki/Quadratic_residue

Quadratic irrational number

MATHEMATICAL CONCEPT

Quadratic surd; Quadratic irrationality; Quadratic Irrational Number; Quadratic irrationalities; Quadratic irrational; Quadratic irrational numbers

In mathematics, a quadratic irrational number (also known as a quadratic irrational, a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers.Jörn Steuding, Diophantine Analysis, (2005), Chapman & Hall, p.

https://en.wikipedia.org/wiki/Quadratic_irrational_number

Residue (complex analysis)

COEFFICIENT OF THE TERM OF ORDER −1 IN THE LAURENT EXPANSION OF A FUNCTION HOLOMORPHIC OUTSIDE A POINT, WHOSE VALUE CAN BE EXTRACTED BY A CONTOUR INTEGRAL

Residue of an analytic function; Residue at a pole; Complex residue; Residue (mathematics)

In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function f\colon \mathbb{C} \setminus \{a_k\}_k \rightarrow \mathbb{C} that is holomorphic except at the discrete points {ak}k, even if some of them are essential singularities.

https://en.wikipedia.org/wiki/Residue_(complex_analysis)

Βικιπαίδεια

Euler's criterion

In number theory, Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime. Precisely,

Let p be an odd prime and a be an integer coprime to p. Then

a^{\tfrac {p-1}{2}}\equiv {\begin{cases}\;\;\,1{\pmod {p}}&{\text{ if there is an integer }}x{\text{ such that }}a\equiv x^{2}{\pmod {p}},\\-1{\pmod {p}}&{\text{ if there is no such integer.}}\end{cases}}

Euler's criterion can be concisely reformulated using the Legendre symbol:

\left({\frac {a}{p}}\right)\equiv a^{\tfrac {p-1}{2}}{\pmod {p}}.

The criterion first appeared in a 1748 paper by Leonhard Euler.

https://en.wikipedia.org/wiki/Euler's criterion