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

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

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

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

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...

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

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

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...

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

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