theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime...

In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f ( x ) {\displaystyle...

In number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusually large number of proofs. Several hundred...

1797 or 1798 in the course of his attempts at proving the law of quadratic reciprocity. Generalizations of the symbol include the Jacobi symbol and Dirichlet...

introduced the square bracket notation [x] in his third proof of quadratic reciprocity (1808). This remained the standard in mathematics until Kenneth...

a quadratic residue or nonresidue modulo n {\displaystyle n} . The Kronecker symbol also satisfies the following versions of quadratic reciprocity law...

nonresidue. The first supplement to the law of quadratic reciprocity is that if p ≡ 1 (mod 4) then −1 is a quadratic residue modulo p, and if p ≡ 3 (mod 4) then...

term "reciprocity law" refers to a long line of more concrete number theoretic statements which it generalized, from the quadratic reciprocity law and...

density theorem. The law of quadratic reciprocity implies that the splitting behaviour of a prime p {\displaystyle p} in a quadratic field depends only on p...

law of quadratic reciprocity and one case of the Fermat polygonal number theorem. He also contributed to the theory of binary and ternary quadratic forms...

century. Gauss proved in this work the law of quadratic reciprocity and developed the theory of quadratic forms. He also introduced some basic notation...

{q-1}{2}}}.} A reciprocity law is a generalization of the law of quadratic reciprocity. There are several different ways to express reciprocity laws. The early...

and applied them to quadratic, cubic, and biquadratic reciprocity laws. For an odd prime number p and an integer a, the quadratic Gauss sum g(a; p) is...

prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the existence...

all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished...

point of the program was Emil Artin's reciprocity law, which generalizes quadratic reciprocity. The Artin reciprocity law applies to a Galois extension of...

and martingales Quadratic reciprocity, a theorem from number theory Quadratic residue, an integer that is a square modulo n Quadratic sieve, a modern...

residue r is a quadratic residue (mod q) if and only if it is a biquadratic residue (mod q). Indeed, the first supplement of quadratic reciprocity states that...

characteristics Helmholtz reciprocity, linear propagation. Reciprocity law (law of reciprocity) in mathematics, including Quadratic reciprocity, a fundamental result...

Reciprocity theorem may refer to: Quadratic reciprocity, a theorem about modular arithmetic Cubic reciprocity Quartic reciprocity Artin reciprocity Weil...

Arithmeticae (1801). In the introduction to the fifth and sixth proofs of quadratic reciprocity (1818) he said that he was publishing these proofs because their...

theorem that has been proved in many different ways is the theorem of quadratic reciprocity. In fact, Carl Friedrich Gauss alone had eight different proofs...

quadratic residue. Although it is not useful computationally, it has theoretical significance, being involved in some proofs of quadratic reciprocity...

with little further discussion. The central topic of quadratic reciprocity and higher reciprocity laws is barely mentioned; this was apparently going to...

Modular_arithmetic#Residue_class Quadratic_residue#Prime_power_modulus Artin symbol Gauss's lemma Quadratic reciprocity deals with squares; higher refers...

all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished...

Gaussian integer, Gaussian rational Quadratic field Cyclotomic field Cubic field Biquadratic field Quadratic reciprocity Ideal class group Dirichlet's unit...

all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished...

period (Fibonacci sequences modulo n) Primitive root modulo n Quadratic reciprocity Quadratic residue Rational reconstruction (mathematics) Reduced residue...

the practical solution of certain congruences, and the law of quadratic reciprocity". Mathematical Proceedings of the Cambridge Philosophical Society...