Law of quadratic reciprocity

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:concerns	gptkb:Quadratic_residues Prime numbers
gptkbp:considers	One of the most important results in elementary number theory
gptkbp:field	gptkb:Number_theory
gptkbp:firstPublished	gptkb:Disquisitiones_Arithmeticae
gptkbp:formedBy	gptkb:Carl_Friedrich_Gauss
gptkbp:generalizes	gptkb:Cubic_reciprocity gptkb:Quartic_reciprocity gptkb:Artin_reciprocity
gptkbp:hasProofsOf	gptkb:Carl_Friedrich_Gauss gptkb:Ernst_Eduard_Kummer gptkb:Leonhard_Euler gptkb:Adrien-Marie_Legendre
https://www.w3.org/2000/01/rdf-schema#label	Law of quadratic reciprocity
gptkbp:influenced	gptkb:Class_field_theory gptkb:Algebraic_number_theory
gptkbp:numberOfProofsByGauss	8
gptkbp:publicationYear	1801
gptkbp:relatedTo	gptkb:Legendre_symbol gptkb:Euler's_criterion Supplementary laws
gptkbp:state	The solvability of the congruence x^2 ≡ p (mod q) is related to the solvability of x^2 ≡ q (mod p) for odd primes p and q
gptkbp:bfsParent	gptkb:Quadratic_reciprocity gptkb:Adrien-Marie_Legendre
gptkbp:bfsLayer	6