Linked from

The 18 pages that link to Quadratic reciprocity, each with the reason it gives.

• Number theoryRelated: It reveals a deep symmetry among prime congruences that simpler divisibility tests do not explain.

• Algebraic number theoryRelated: Its proofs in number fields reveal how field extensions encode congruence laws.

• Adrien-Marie LegendreRelated: Legendre formulated a proof of this central theorem, later completed rigorously by Gauss.

• Class field theoryNarrower topic: Its generalizations became the reciprocity laws that class field theory unifies.

• Disquisitiones ArithmeticaeBroader topic: Gauss proves this central theorem and develops several proofs and applications.

• Legendre symbolRelated: The symbol made this reciprocity relation concise and calculable.

• Quadratic residueRelated: It lets residue questions between primes answer one another.

• Emil ArtinCompared with: Artin reciprocity extends the pattern of exchanging arithmetic data seen in this classical law.

• Ernst KummerRelated: The reciprocity tradition Kummer inherited inspired his extensions to higher powers.

• Euler's criterionRelated: Euler's criterion is an elementary tool in the theory that reciprocity organizes.

• Jacobi symbolRelated: Reciprocity laws let computations exchange numerator and denominator, driving efficient Jacobi-symbol algorithms.

• Fermat's theorem on sums of two squaresRelated: It gives a broader framework for the residue condition underlying the theorem.

• Helmut HasseRelated: Local reciprocity generalizes this classical arithmetic pattern in Hasse’s framework.

• Kronecker–Weber theoremRelated: Cyclotomic fields provide a field-theoretic setting for reciprocity phenomena involving quadratic extensions.

• Sophie Germain primeRelated: Residue constraints from quadratic reciprocity can restrict prime patterns involving p and 2p + 1.

• Hasse–Minkowski theoremRelated: Its reciprocity pattern is a precedent for global compatibility among local data.

• Cubic reciprocityCompared with: Cubic reciprocity generalizes its exchange principle from squares to cubes.

• Gotthold EisensteinRelated: Eisenstein developed a proof using cyclotomic ideas and contributed to reciprocity theory.