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Branch of pure mathematics
Number theory is a branch of mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers
Number_theory
Study of subsets of integers and behavior under addition
Additive number theory is the subfield of number theory concerning the study of subsets of integers and their behavior under addition. More abstractly
Additive_number_theory
Exploring properties of the integers with complex analysis
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.
Analytic_number_theory
Theory of subatomic structure
force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions
String_theory
Numbers expressible as integrals of algebraic functions
In mathematics, specifically number theory, a period or algebraic period is a complex number that can be expressed as an integral of an algebraic function
Period_(number_theory)
Branch of number theory
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations
Algebraic_number_theory
discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey theory, dynamical systems, and partial differential
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Study of algorithms for performing number theoretic computations
number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory
Computational_number_theory
Study of numbers that are not solutions of polynomials with rational coefficients
Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation
Transcendental_number_theory
Number of partitions of an integer
In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because
Partition function (number theory)
Partition_function_(number_theory)
Natural number
identity, meaning that any number multiplied by 1 equals the same number. 1 is by convention not considered a prime number. In digital technology, 1 represents
1
Multiplicative number theory is a subfield of analytic number theory that deals with prime numbers and with factorization and divisors. The focus is usually
Multiplicative_number_theory
Condition under which an integer is a quadratic residue
Gauss's lemma in number theory gives a condition for an integer to be a quadratic residue. Although it is not useful computationally, it has theoretical
Gauss's_lemma_(number_theory)
topics in number theory. See also: List of recreational number theory topics Topics in cryptography Composite number Highly composite number Even and odd
List_of_number_theory_topics
Topics referred to by the same term
Prime number theory may refer to: Prime number Prime number theorem Number theory Fundamental theorem of arithmetic, which explains prime factorization
Prime_number_theory
Used to count, measure, and label
term which may also refer to number theory, the study of the properties of numbers. Viewing the concept of zero as a number required a fundamental shift
Number
Branch of mathematics that studies sets
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any
Set_theory
Decomposition of an integer as a sum of positive integers
In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive
Integer_partition
Number divisible only by 1 and itself
smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime
Prime_number
Branch of elementary mathematics
modern number theory include elementary number theory, analytic number theory, algebraic number theory, and geometric number theory. Elementary number theory
Arithmetic
coefficients. algebraic number field See number field. algebraic number theory Algebraic number theory analytic number theory Analytic number theory Artin The Artin
Glossary_of_number_theory
Mathematical theory by Shinichi Mochizuki
is "an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve". The theory was made public in a series of four preprints
Inter-universal Teichmüller theory
Inter-universal_Teichmüller_theory
Study of discrete mathematical structures
Originally a part of number theory and analysis, partition theory is now considered a part of combinatorics or an independent field. Order theory is the study
Discrete_mathematics
Topics referred to by the same term
Unsolved Problems in Number Theory may refer to: Unsolved problems in mathematics in the field of number theory. A book with this title by Richard K. Guy
Unsolved Problems in Number Theory
Unsolved_Problems_in_Number_Theory
Branch of mathematics that studies the properties of groups
groups. Group theory has three main historical sources: number theory, the theory of algebraic equations, geometry, and analysis. The number-theoretic strand
Group_theory
Number with a real and an imaginary part
for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example). Unlike real functions
Complex_number
Theorem in number theory
In number theory, Lagrange's theorem is a statement named after Joseph-Louis Lagrange about how frequently a polynomial over the integers may evaluate
Lagrange's theorem (number theory)
Lagrange's_theorem_(number_theory)
Creating sequence of numbers that cannot be predicted
Martin; Mehic, Miralem (2020). "Quantum Random Number Generation". Quantum Random Number Generation: Theory and Practice. Springer International Publishing
Random_number_generation
Axiomatic system
Typographical Number Theory (TNT) is a formal axiomatic system describing the natural numbers that appears in Douglas Hofstadter's book Gödel, Escher
Typographical_Number_Theory
Rational-number approximation of a real number
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus
Diophantine_approximation
Supposition or system of ideas intended to explain something
A theory is, in general, any hypothesis or set of ideas about something, formed in any number of ways through any sort of reasoning for any sort of reason
Theory
Subfield of computer science and mathematics
computational economics, computational geometry, and computational number theory and algebra. Work in this field is often distinguished by its emphasis
Theoretical_computer_science
Branch of discrete mathematics
fields, ranging from algebra to probability, from functional analysis to number theory, etc. These connections shed the boundaries between combinatorics and
Combinatorics
Number
year numbering, the year 1 BC is numbered 0, the year 2 BC is numbered −1, and so forth. Grammatical number Mathematical constant Number theory Peano
0
2.71828…, base of natural logarithms
percentage, so for 5% interest, R = 5/100 = 0.05. The number e itself also has applications in probability theory, in a way that is not obviously related to exponential
E_(mathematical_constant)
Application of geometry in number theory
Geometry of numbers, also known as geometric number theory, is the part of number theory which uses geometry for the study of algebraic numbers. Typically
Geometry_of_numbers
Field of knowledge
and everyday life. There are many areas of mathematics, including number theory (the study of integers and their properties), algebra (the study of
Mathematics
solve number theory problems. In doing so, he united two disparate branches of mathematics and introduced a new field of study, analytic number theory. In
Contributions of Leonhard Euler to mathematics
Contributions_of_Leonhard_Euler_to_mathematics
Number, approximately 3.14
mechanics, and electromagnetism. It also appears in areas such as number theory, statistics, and in modern mathematical analysis: π is ubiquitous. The
Pi
Class of integer
of powers conjecture – Disproved conjecture in number theory Generalized taxicab number – Smallest number expressable as the sum of j numbers to the kth
Taxicab_number
Free and open-source software portal NTL is a C++ library for doing number theory. NTL supports arbitrary length integer and arbitrary precision floating
Number_Theory_Library
Integer having a non-trivial divisor
incompatibility (help) Long, Calvin T. (1972), Elementary Introduction to Number Theory (2nd ed.), Lexington: D. C. Heath and Company, LCCN 77-171950 McCoy
Composite_number
Natural number
meaning has been identified, though theories include that is the year of Prohibition ending in the US and the number of letters in quality statement also
33_(number)
Theorem in number theory that gives a bound on a Diophantine approximation
In number theory, Hurwitz's theorem, named after Adolf Hurwitz, gives a bound on a Diophantine approximation. The theorem states that for every irrational
Hurwitz's theorem (number theory)
Hurwitz's_theorem_(number_theory)
algebraic number theory, a fundamental unit is a generator (modulo the roots of unity) for the unit group of the ring of integers of a number field, when
Fundamental unit (number theory)
Fundamental_unit_(number_theory)
Branch of algebra
algebraic number theory, which provide many natural examples of commutative rings, have driven much of the development of commutative ring theory, which
Ring_theory
Number used for counting
the study of the ways to perform basic operations on these number systems. Number theory is the study of the properties of these operations and their
Natural_number
Behrend's theorem (number theory) Bertrand's postulate (number theory) Birch's theorem (algebraic number theory) Bombieri's theorem (number theory) Bombieri–Friedlander–Iwaniec
List_of_theorems
Subfield of number theory
In mathematics, Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions about the integers and
Probabilistic_number_theory
Branch of mathematics
Abstract analytic number theory is a branch of mathematics which takes the ideas and techniques of classical analytic number theory and applies them to
Abstract analytic number theory
Abstract_analytic_number_theory
Natural number
natural number and positive integer following 53 and preceding 55. As a multiple of 2 but not of 4, 54 is an oddly even number and a composite number. 54
54_(number)
Branch of mathematics that studies abstract algebraic structures
module theory, analytic number theory, differential geometry, operator theory, algebraic combinatorics and topology. The success of representation theory has
Representation_theory
In mathematics, a non-algebraic number
"Number theory and formal languages". In Hejhal, D.A.; Friedman, Joel; Gutzwiller, M.C.; Odlyzko, A.M. (eds.). Emerging Applications of Number Theory.
Transcendental_number
Natural number
(2005). An Introduction to Number Theory. Springer. p. 117. ISBN 978-1-85233-917-3. Lozano-Robledo, Álvaro (2019). Number Theory and Geometry: An Introduction
1729_(number)
Swiss mathematician (1707–1783)
studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis
Leonhard_Euler
algebraic number theory, a modulus (plural moduli) (or cycle, or extended ideal) is a formal product of places of a global field (i.e. an algebraic number field
Modulus (algebraic number theory)
Modulus_(algebraic_number_theory)
Branch of applied probability theory
Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses expected utility and probability
Decision_theory
Academic journal
Algebra & Number Theory is a peer-reviewed mathematics journal published by the nonprofit organization Mathematical Sciences Publishers. It was launched
Algebra_&_Number_Theory
Australian and American mathematician (born 1975)
differential equations, combinatorics, harmonic analysis, and additive number theory. He is a professor of mathematics at the University of California, Los
Terence_Tao
Branch of mathematics studying functions of a complex variable
branches of mathematics, including real analysis, algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics
Complex_analysis
In algebra and number theory, a distribution is a function on a system of finite sets into an abelian group which is analogous to an integral: it is thus
Distribution_(number_theory)
field level. This technique is applied in algebraic number theory and modular representation theory. Hurwitz quaternion order – An example of ring order
Order_(ring_theory)
Number equal to the sum of its proper divisors
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number
Perfect_number
Mathematical connection between field theory and group theory
mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the
Galois_theory
Number system extending the rational numbers
In number theory, given a prime number p, the p-adic numbers form an extension of the rational numbers that is distinct from the real numbers, though
P-adic_number
Branch of mathematics that studies dynamical systems
theory. Ergodic theory has fruitful connections with harmonic analysis, Lie theory (representation theory, lattices in algebraic groups), and number theory
Ergodic_theory
Characterization of how many integers are prime
and B are unspecified constants. In the second edition of his book on number theory (1808) he then made a more precise conjecture, with A = 1 and B = −1
Prime_number_theorem
Index of articles associated with the same name
In number theory, a symbol is any of many different generalizations of the Legendre symbol. This article describes the relations between these various
Symbol_(number_theory)
Academic subfield of computer science
In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation
Theory_of_computation
Branch of algebraic number theory concerned with abelian extensions
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions
Class_field_theory
Fewest edge crossings in drawing of a graph
In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph
Crossing number (graph theory)
Crossing_number_(graph_theory)
Integers have unique prime factorizations
to Number Theory (2nd ed.), Lexington: D. C. Heath and Company, LCCN 77-171950. Pettofrezzo, Anthony J.; Byrkit, Donald R. (1970), Elements of Number Theory
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Group-like structure appearing in global fields
number theory, Part II, 235–286, Math. Centre Tracts, 155, Math. Centrum, Amsterdam, 1982. MR 0702519 H. C. Williams: Continued fractions and number-theoretic
Infrastructure (number theory)
Infrastructure_(number_theory)
Average uncertainty in variable's states
In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential
Entropy_(information_theory)
Ways to estimate the size of sifted sets of integers
Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers
Sieve_theory
French mathematician, physicist, and philosopher
research (see Honors in number theory). Germain's best work was in number theory, and her most significant contribution to number theory dealt with Fermat's
Sophie_Germain
Concept in algebraic number theory
In number theory, Heegner numbers are square-free positive integers d {\displaystyle d} such that the imaginary quadratic field Q ( − d ) {\displaystyle
Heegner_number
Topics referred to by the same term
axiom of set theory asserting the non-existence of certain infinite chains of sets Partition regularity Regular cardinal, a cardinal number that is equal
Regular
Property of being an even or odd number
even number, and the Taylor series of an odd function contains only terms whose exponent is an odd number. In combinatorial game theory, an evil number is
Parity_(mathematics)
Class of irrational numbers
In number theory, a Liouville number is a real number x {\displaystyle x} with the property that, for every positive integer n {\displaystyle n} , there
Liouville_number
recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative: many famous topics in number theory have origins
List of recreational number theory topics
List_of_recreational_number_theory_topics
Natural number
"Irregularities in the distributions of finite sequences". Journal of Number Theory. 2 (2): 152–161. Bibcode:1970JNT.....2..152B. doi:10.1016/0022-314X(70)90015-6
17_(number)
Hungarian mathematician (1913–1996)
discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered
Paul_Erdős
Describes approximate behavior of a function
analytic number theory, big O notation expresses bounds on the growth of an arithmetical function, as for the remainder term in the prime number theorem
Big_O_notation
Number that is abundant but not semiperfect
In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including
Weird_number
Mathematics independent of applications
mathematics. Plato helped to create the gap between "arithmetic", now called number theory, and "logistic", now called arithmetic. Plato regarded logistic (arithmetic)
Pure_mathematics
Euler's totient function (or Euler phi (φ) function) in number theory, counting the number of coprime integers less than an integer. Euler hypergeometric
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
In number theory, Weyl's inequality, named for Hermann Weyl, states that if M, N, a and q are integers, with a and q coprime, q > 0, and f is a real polynomial
Weyl's inequality (number theory)
Weyl's_inequality_(number_theory)
Integer filtered out using a sieve similar to that of Eratosthenes
In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the sieve of Eratosthenes
Lucky_number
Branch of mathematics concerning probability
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations
Probability_theory
Book about number theory
Basic Number Theory is an influential book by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on
Basic_Number_Theory
In mathematics, element with a multiplicative inverse
in commutative ring theory, Princeton University Press, ISBN 978-0-691-12748-4, MR 2330411 Weil, André (1974). Basic number theory. Grundlehren der mathematischen
Unit_(ring_theory)
Multiplicative function in number theory
function μ ( n ) {\displaystyle \mu (n)} is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also
Möbius_function
Figurate number
The triangular lattice representing the n {\displaystyle n} th triangular number contains n {\displaystyle n} rows: the first row contains one point, the
Triangular_number
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
German mathematician (1849–1917)
known for his contributions to the theory of elliptic functions, differential equations, number theory, and to group theory. He is known for the famous determinantal
Ferdinand_Georg_Frobenius
number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is
Lists_of_mathematics_topics
Mathematical manifold theory
numbers, it can be applied to questions in number theory. In arithmetic situations, the tools of p-adic Hodge theory have given alternative proofs of, or analogous
Hodge_theory
Number that is not a ratio of integers
of the most famous open problems in number theory" (PDF). Waldschmidt, Michel (2022). "Transcendental Number Theory: recent results and open problems"
Irrational_number
In number theory, measure of non-unique factorization
order of the group, which is finite, is called the class number of K {\displaystyle K} . The theory extends to Dedekind domains and their fields of fractions
Ideal_class_group
NUMBER THEORY
NUMBER THEORY
Surname or Lastname
English
English : variant of Sumpter.Fort Sumter, SC, was named in honor of Thomas Sumter, known as the ‘Gamecock of the Revolution’ for the fear he inspired in the British and Tory forces and the pivotal role he played in key American victories. Born in 1734 near Charlottesville, VA, he was of Welsh heritage; his ancestors probably emigrated to America in the late 17th century.
Surname or Lastname
English
English : habitational name from any of the various places so called from their situation on a stream with this name. Humber is a common prehistoric river name, of uncertain origin and meaning.
Female
English
English name derived from the vocabulary word, summer, from Old English sumor, SUMMER means "summer," the hot season of the year.
Girl/Female
American, Arabic, Australian, British, Chinese, English, Hebrew
The Warmest Season of the Year; Summer Season; Name of the Season; Summer; The Hot Season of the Year
Female
Native American
Native American Algonquin name NUMEES means "sister."
Male
English
English form of Norman Germanic Huncberct, possibly HUMBERT means "bright support."Â
Surname or Lastname
English
English : habitational name from Bamber Bridge in Lancashire, probably named with Old English bēam ‘tree trunk’, ‘beam’ + brycg ‘bridge’.German : nickname for a short fat person.
Boy/Male
Australian
Number One
Girl/Female
English American
Born during the summer.
Girl/Female
Arabic, Australian, Muslim
Figure; Number
Surname or Lastname
English
English : perhaps a variant of Pamber, a habitational name from a place in Hampshire named Pamber, from Old English penn ‘fold’, ‘enclosure’ + beorg ‘hill’.
Surname or Lastname
English
English : occupational name for a summoner, an official who was responsible for ensuring the appearance of witnesses in court, Middle English sumner, sumnor.William Sumner came to Dorchester, MA, from England in about 1635. His descendants include U.S. Senator Charles Sumner, a major force in the struggle to end slavery, who was born in 1811 in Boston.
Boy/Male
Hindu, Indian
Number
Girl/Female
Muslim American Arabic English Gaelic
Jewel. Amber stone.
Male
German
German byname BAMBER means "short and fat."Â
Boy/Male
Tamil
The number
Boy/Male
Hindu
The number
Surname or Lastname
English and German
English and German : from Middle English sum(m)er, Middle High German sumer ‘summer’, hence a nickname for someone of a warm or sunny disposition, or for someone associated with the season of summer in some other way.English : assimilated variant of Sumner.English : assimilated variant of Sumpter.Irish (Leinster and Munster) : Anglicization (part translation) of Gaelic Ó Samhraidh ‘descendant of Samhradh’, a byname meaning ‘summer’. The Gaelic name is also Anglicized as O’Sawrie, O’Sawra.German : from Middle High German summer ‘woven basket’ and, by extension, a measure of grain; also ‘drum’, hence a metonymic occupational name or nickname from any of these senses.
Girl/Female
Hindu, Indian
Number; Definition
Boy/Male
Indian
Ten (Number)
NUMBER THEORY
NUMBER THEORY
Female
English
English pet form of Latin Cynthia, CINDY means "woman from Kynthos."Â
Boy/Male
Tamil
Cloud
Boy/Male
British, English
Divine Friend
Boy/Male
Tamil
Krishanu | கà¯à®°à®¿à®·à®¾à®¨à¯
Flame, Fire
Girl/Female
English French
Courtyard within castle walls; steward or public official. Surname or given name.
Female/Male/Unisex
Korean
Korean unisex name ISEUL means "dew."
Boy/Male
Australian, Vietnamese
Fame; Prestige
Girl/Female
Indian
Wish, Desire, Aspiration
Boy/Male
Hindu, Indian, Sanskrit
Devoted to Krishna
Boy/Male
Hindu, Indian, Punjabi, Sikh, Tamil
Winner; Warrior of Battle; The Brave Warrior
NUMBER THEORY
NUMBER THEORY
NUMBER THEORY
NUMBER THEORY
NUMBER THEORY
n.
Timber sawed or split into the form of beams, joists, boards, planks, staves, hoops, etc.; esp., that which is smaller than heavy timber.
n.
To amount; to equal in number; to contain; to consist of; as, the army numbers fifty thousand.
n.
An African wading bird (Scopus umbretta) allied to the storks and herons. It is dull dusky brown, and has a large occipital crest. Called also umbrette, umbre, and umber bird.
v. t.
To color with umber; to shade or darken; as, to umber over one's face.
n.
pl. of Number. The fourth book of the Pentateuch, containing the census of the Hebrews.
n.
Number; -- often abbrev. No.
n.
To give or apply a number or numbers to; to assign the place of in a series by order of number; to designate the place of by a number or numeral; as, to number the houses in a street, or the apartments in a building.
a.
Of or pertaining to umber; resembling umber; olive-brown; dark brown; dark; dusky.
n.
One who numbers.
v. t.
To cumber.
imp. & p. p.
of Number
imp. & p. p.
of Numb
n.
That which is regulated by count; poetic measure, as divisions of time or number of syllables; hence, poetry, verse; -- chiefly used in the plural.
v. t.
To keep or carry through the summer; to feed during the summer; as, to summer stock.
a.
Of or pertaining to umber; like umber; as, umbery gold.
n.
A numeral; a word or character denoting a number; as, to put a number on a door.
n.
The distinction of objects, as one, or more than one (in some languages, as one, or two, or more than two), expressed (usually) by a difference in the form of a word; thus, the singular number and the plural number are the names of the forms of a word indicating the objects denoted or referred to by the word as one, or as more than one.
b. t.
To fill or encumber with lumber; as, to lumber up a room.
n.
India rubber; caoutchouc.
v. t.
See Encumber.