Quadratic Reciprocity Law

URI: https://gptkb.org/entity/Quadratic_Reciprocity_Law

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:category	Reciprocity laws Theorems in number theory
gptkbp:concerns	gptkb:Legendre_symbol prime numbers quadratic residues
gptkbp:field	number theory
gptkbp:firstPublished	gptkb:Disquisitiones_Arithmeticae
gptkbp:formedBy	gptkb:Carl_Friedrich_Gauss
gptkbp:generalizes	gptkb:Cubic_reciprocity gptkb:Quartic_reciprocity gptkb:Artin_reciprocity_law
gptkbp:hasProofsOf	gptkb:Carl_Friedrich_Gauss gptkb:Ernst_Eduard_Kummer gptkb:Leonhard_Euler gptkb:Adrien-Marie_Legendre
gptkbp:hasSupplementaryLaw	gptkb:First_Supplementary_Law gptkb:Second_Supplementary_Law
https://www.w3.org/2000/01/rdf-schema#label	Quadratic Reciprocity Law
gptkbp:isFundamentalTo	algebraic number theory elementary number theory
gptkbp:numberOfProofsByGauss	8
gptkbp:publicationYear	1801
gptkbp:relatedTo	gptkb:Kronecker_symbol gptkb:Chinese_Remainder_Theorem gptkb:Eisenstein_reciprocity gptkb:Hilbert_symbol
gptkbp:state	For distinct odd primes p and q, (p/q)(q/p) = (−1)^((p−1)(q−1)/4)
gptkbp:bfsParent	gptkb:Number_Theory
gptkbp:bfsLayer	7