This HTML5 document contains 267 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dcthttp://purl.org/dc/terms/
yago-reshttp://yago-knowledge.org/resource/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
n4http://dbpedia.org/resource/File:
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
freebasehttp://rdf.freebase.com/ns/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
n13http://en.wikipedia.org/wiki/
dbphttp://dbpedia.org/property/
dbchttp://dbpedia.org/resource/Category:
provhttp://www.w3.org/ns/prov#
n15http://sw.cyc.com/concept/
xsdhhttp://www.w3.org/2001/XMLSchema#
goldhttp://purl.org/linguistics/gold/
dbrhttp://dbpedia.org/resource/
n8http://d-nb.info/gnd/

Statements

Subject Item
dbr:Number_theory
rdf:type
owl:Thing dbo:Organisation
rdfs:label
Number theory
rdfs:comment
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers).
owl:differentFrom
dbr:Numerology
owl:sameAs
n8:4067277-3 freebase:m.05dkb n15:Mx4rwEQVt5wpEbGdrcN5Y29ycA yago-res:Number_theory
dbp:wikiPageUsesTemplate
dbt:Sfn dbt:Wikiquote dbt:Commons_category-inline dbt:Number_theory dbt:For dbt:Citizendium dbt:Computer_science dbt:Pi dbt:Expand_section dbt:Further dbt:Reflist dbt:Refbegin dbt:Refend dbt:Distinguish dbt:Main dbt:Cite_journal dbt:Cite_book dbt:Cite_encyclopedia dbt:Areas_of_mathematics dbt:Specify dbt:Cite_web dbt:Harvid dbt:Math_topics_TOC dbt:Authority_control dbt:Sic dbt:Short_description
dct:subject
dbc:Number_theory
gold:hypernym
dbr:Branch
prov:wasDerivedFrom
n13:Number_theory?oldid=1072405630&ns=0
dbo:wikiPageID
21527
dbo:wikiPageLength
83711
dbo:wikiPageRevisionID
1072405630
dbo:wikiPageWikiLink
dbr:Babylonian_astronomy dbr:Gotthold_Ephraim_Lessing dbr:Egypt dbr:Hilbert's_tenth_problem dbr:University_of_Chicago_Press n4:Lehmer_sieve.jpg dbr:Archimedes's_cattle_problem dbr:Finite_field dbr:Adrien-Marie_Legendre dbr:Computably_enumerable dbr:Identity_(mathematics) dbr:Elliptic_curve dbr:Babylonian_mathematics dbr:Computer_scientist dbr:Plato dbr:Euclid's_Elements dbr:Chinese_remainder_theorem dbr:Bernhard_Riemann dbr:Ernst_Kummer dbr:Heuristic dbr:Computer_science dbr:Elliptic_integral dbr:Theaetetus_(dialogue) dbr:Theaetetus_(mathematician) dbr:Plimpton_322 n4:Leonhard_Euler.jpg dbr:Euclid dbr:Pythagorean_theorem dbr:Cramér's_conjecture dbr:Landau_prime_ideal_theorem dbr:Analytic_number_theory dbr:Twin_prime dbr:Glossary_of_arithmetic_and_diophantine_geometry dbr:Group_theory dbr:Academic_Press dbr:Real_number dbr:Torus dbr:Quadratic_form dbr:Power_series dbr:Christian_Goldbach dbr:Numerical_analysis dbr:Henry_Thomas_Colebrooke dbr:Transcendental_number dbr:Turing_machine dbr:Transcendental_number_theory dbr:Muhammad_ibn_Musa_al-Khwarizmi dbr:Quadratic_reciprocity dbr:Bhāskara_II dbr:Atle_Selberg dbr:Pythagorean_triple dbr:Perfect_number n4:Hevelius_Selenographia_frontispiece.png dbr:Pythagoreanism dbr:Langlands_program dbr:Modular_form dbr:Eratosthenes dbr:Pentagonal_number dbr:Disquisitiones_Arithmeticae dbr:Goldbach's_conjecture dbr:Amicable_numbers n4:ErnstKummer.jpg dbr:Dirichlet's_theorem_on_arithmetic_progressions dbr:Joseph-Louis_Lagrange dbr:Primality_test dbr:Paul_Erdős dbr:Akkadian_language n4:Spirale_Ulam_150.jpg dbr:Oxford_University_Press dbr:Distribution_(number_theory) dbr:Hardy–Littlewood_circle_method dbr:Faltings's_theorem dbr:Undergraduate_Texts_in_Mathematics dbr:Fermat_Prize dbr:Évariste_Galois dbr:Sophie_Germain dbr:Arithmetica dbr:Independence_(probability_theory) dbr:Norm_(mathematics) dbr:Algebra dbr:Cambridge_University_Press dbr:Triangular_number dbr:Floating-point_arithmetic dbr:Divisor dbr:Ergodic_theory dbr:Elementary_proof dbr:Lagrange's_four-square_theorem dbr:Wiley_(publisher) dbr:Larsa dbr:Pure_mathematics dbr:Euclidean_algorithm dbr:Eusebius dbr:Vedas dbr:Peano_axioms dbr:Qusta_ibn_Luqa dbr:Donald_Knuth dbr:Graduate_Texts_in_Mathematics dbr:Cole_Prize dbr:Irrational_number n4:Paul_Erdos_with_Terence_Tao.jpg dbr:Fibonacci dbr:Ancient_Egyptian_mathematics dbr:Partition_function_(number_theory) dbr:Square_root_of_2 dbr:Pearson_Education dbr:Algebraic_number dbr:Algebraic_number_field dbr:Valuation_(algebra) dbr:Algebraic_number_theory dbr:Abelian_group dbr:Root_of_unity dbr:Al-Karaji n4:Carl_Friedrich_Gauss.jpg n4:Peter_Gustav_Lejeune_Dirichlet.jpg dbr:Renaissance dbr:Curve dbr:Diophantine_equation dbr:Arithmetic dbr:Wiener–Ikehara_theorem dbr:Pappus_of_Alexandria dbr:Pierre_de_Fermat dbr:Abelian_and_Tauberian_theorems dbr:Diophantine_geometry dbr:P-adic_number dbr:Recreational_mathematics dbr:Probabilistic_method dbc:Number_theory dbr:Class_field_theory dbr:Diophantus dbr:Leonhard_Euler dbr:Additive_number_theory dbr:Geometry_of_numbers dbr:Diophantine_approximation dbr:Brāhmasphuṭasiddhānta dbr:Ideal_(ring_theory) dbr:Waring's_problem dbr:Algebraic_surface dbr:Euclid's_theorem dbr:Computational_complexity_theory dbr:Fermat's_Last_Theorem dbr:Chakravala_method dbr:Theodorus_of_Cyrene dbr:E_(mathematical_constant) dbr:Figurate_number dbr:Group_(mathematics) dbr:Ibn_al-Haytham dbr:Iwasawa_theory dbr:Princeton_University_Press n4:ECClines-3.svg dbr:Al-Ma'mun dbr:Thales_of_Miletus dbr:Cryptography dbr:Fermat's_little_theorem dbr:Leonard_Eugene_Dickson dbr:Sieve_theory dbr:Arithmetic_function dbr:American_Mathematical_Society dbr:Algebraic_variety dbr:Mathematical_Association_of_America dbr:Commensurability_(mathematics) dbr:Magic_square dbr:Wilson's_theorem dbr:Prime_ideal dbr:Sunzi_Suanjing dbr:Kuṭṭaka dbr:Springer_Publishing dbr:Square_number dbr:Springer_Science+Business_Media dbr:Model_theory n4:ModularGroup-FundamentalDomain.svg dbr:Epigram dbr:Polygonal_number dbr:Proof_by_exhaustion dbr:American_Oriental_Society dbr:Proof_by_infinite_descent dbr:Hippasus dbr:Dedekind_zeta_function dbr:Galois_group dbr:Cube_(algebra) dbr:Encyclopedia_of_Mathematics dbr:Leopold_Kronecker dbr:Integer n4:Plimpton_322.jpg dbr:Riemann_hypothesis dbr:RSA_(cryptosystem) dbr:Jacobi's_four-square_theorem dbr:Elementary_arithmetic dbr:Discrete_mathematics dbr:Prime_number dbr:Pell's_equation dbr:Prime_number_theorem dbr:Peter_Gustav_Lejeune_Dirichlet dbr:Galois_theory n4:Pierre_de_Fermat.png dbr:Pi dbr:Complex_analysis dbr:Algebraic_curve n4:Diophantus-cover.jpg n4:Disqvisitiones-800.jpg dbr:Rational_function dbr:Automorphic_form dbr:Computability dbr:Brahmagupta dbr:Rational_number dbr:Abstract_algebra dbr:Mathematical_logic dbr:Carl_Friedrich_Gauss dbr:Rational_point dbr:Algebraic_function_field dbr:Iamblichus dbr:Gotthold_Eisenstein n4:Andrew_wiles1-3.jpg dbr:D._C._Heath_and_Company dbr:Aryabhata n4:Complex_zeta.jpg dbr:Congruence_relation dbr:Ring_(mathematics) dbr:Riemann_zeta_function dbr:Archimedes dbr:Algebraic_integer dbr:Number dbr:Greatest_common_divisor dbr:L-function dbr:Pythagoras dbr:Finite_group
dbo:abstract
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, for example, as approximated by the latter (Diophantine approximation). The older term for number theory is arithmetic. By the early twentieth century, it had been superseded by "number theory". (The word "arithmetic" is used by the general public to mean "elementary calculations"; it has also acquired other meanings in mathematical logic, as in Peano arithmetic, and computer science, as in floating-point arithmetic.) The use of the term arithmetic for number theory regained some ground in the second half of the 20th century, arguably in part due to French influence. In particular, arithmetical is commonly preferred as an adjective to number-theoretic.
foaf:isPrimaryTopicOf
n13:Number_theory