ⓘ List of number theory topics

                                     

ⓘ List of number theory topics

  • Highly composite number
  • Composite number
  • Parity
  • Even and odd numbers
  • Least common multiple
  • Extended Euclidean algorithm
  • Divisor, aliquot part
  • Greatest common divisor
  • Coprime
  • Euclids lemma
  • Table of divisors
  • Bezouts identity, Bezouts lemma
  • Euclidean algorithm
  • Prime number, prime power
  • Bonses inequality
  • Prime factor
  • Table of prime factors
  • Formula for primes
  • Factorization
  • RSA number
  • Square-free integer
  • Square-free polynomial
  • Fundamental theorem of arithmetic
  • Square-free
  • Power of two
  • Integer-valued polynomial
  • Square number
                                     

1. Fractions

  • Farey sequence
  • Cyclic number
  • Dyadic fraction
  • Ford circle
  • Irreducible fraction = in lowest terms
  • Unit fraction
  • Stern–Brocot tree
  • Rational number
  • Recurring decimal
  • Dedekind sum
  • Egyptian fraction
                                     

2. Modular arithmetic

  • Montgomery reduction
  • Modular exponentiation
  • Fermats little theorem
  • Method of successive substitution
  • Proofs of Fermats little theorem
  • Linear congruence theorem
  • Chinese remainder theorem
  • Eulers totient function
  • Nontotient
  • Noncototient
  • Fermat quotient
  • Eulers theorem
  • Multiplicative order
  • Discrete logarithm
  • Wilsons theorem
  • Primitive root modulo n
  • Gausss lemma number theory
  • Quadratic residue
  • Eulers criterion
  • Legendre symbol
  • Congruence of squares
  • Mod n cryptanalysis
  • Luhn formula
                                     

3. Arithmetic functions

  • Mobius function
  • Erdos–Kac theorem
  • Additive function
  • Multiplicative function
  • Mobius inversion formula
  • Dirichlet convolution
  • Landaus function
  • Bell numbers
  • Pentagonal number theorem
  • Divisor function
  • Partition function number theory
  • Integer partition
  • Liouville function
  • Bell series
  • Lambert series
                                     

4. Analytic number theory: additive problems

  • Twin prime
  • Bruns constant
  • Prime quadruplet
  • Goldbachs conjecture
  • Cousin prime
  • Sexy prime
  • Goldbachs weak conjecture
  • Prime triplet
  • Cunningham chain
  • Sophie Germain prime
  • Bateman–Horn conjecture
  • Brahmagupta–Fibonacci identity
  • Eulers four-square identity
  • Warings problem
  • Lagranges four-square theorem
  • Hardy–Littlewood circle method
  • Second Hardy–Littlewood conjecture
  • Schinzels hypothesis H
  • Taxicab number
  • Generalized taxicab number
  • Sierpinski number
  • Schnirelmann density
  • Sumset
  • Landau–Ramanujan constant
  • Seventeen or Bust
  • Cabtaxi number
  • Nivens constant
                                     

5. L-functions

  • Hurwitz zeta function
  • Basel problem on ζ2
  • Riemann zeta function
  • Agoh–Giuga conjecture
  • Von Staudt–Clausen theorem
  • Bernoulli number
  • Dirichlet series
  • Prime-counting function
  • Prime number theorem
  • Euler product
  • Meissel–Lehmer algorithm
  • Legendres constant
  • Bertrands postulate
  • Offset logarithmic integral
  • Proof of Bertrands postulate
  • Skewes number
  • Proof that the sum of the reciprocals of the primes diverges
  • Cramers conjecture
  • Riemann hypothesis
  • De Bruijn–Newman constant
  • Generalized Riemann hypothesis
  • Critical line theorem
  • Hilbert–Polya conjecture
  • Mertens function, Mertens conjecture, Meissel–Mertens constant
  • Dirichlet L-series
  • Siegel zero
  • Dirichlet character
  • Elliott–Halberstam conjecture
  • Dirichlets theorem on arithmetic progressions
  • Linniks theorem
  • Local zeta function
  • Weil conjectures
  • Functional equation L-function
  • Chebotarevs density theorem
  • Cusp form
  • Hecke operator
  • modular group
  • Modular curve
  • Eisenstein series
  • Modular form
  • Ramanujan–Petersson conjecture
  • Congruence subgroup
  • Selberg trace formula
  • Birch and Swinnerton-Dyer conjecture
  • Automorphic form
  • modularity theorem
  • Artin conjecture
  • Sato–Tate conjecture
  • Langlands program


                                     

6. Diophantine equations

  • Elliptic curve
  • Pythagorean triple
  • Arithmetic of abelian varieties
  • Congruent number
  • Pells equation
  • Mazurs torsion theorem
  • Mordell–Weil theorem
  • Mordell curve
  • Elliptic divisibility sequences
  • Nagell–Lutz theorem
  • Mordell conjecture
  • Eulers sum of powers conjecture
  • Fermats Last Theorem
  • Matiyasevichs theorem
  • Catalans conjecture
  • abc Conjecture
  • Hasse principle
  • Diophantine set
  • Pillais conjecture
  • Hundred Fowls Problem
  • 1729


                                     

7. Diophantine approximation

  • Integer square root
  • Quadratic irrational
  • Irrational number
  • Square root of two
  • Algebraic number
  • Salem number
  • Davenport–Schmidt theorem
  • Pisot–Vijayaraghavan number
  • Hilberts seventh problem
  • Lindemann–Weierstrass theorem
  • e mathematical constant
  • Transcendental number
  • Proof that e is irrational
  • pi, list of topics related to pi
  • Squaring the circle
  • Gelfond–Schneider theorem
  • Erdos–Borwein constant
  • Generalized continued fraction
  • Khinchins constant
  • Continued fraction
  • Liouville number
  • Mathematical constant sorted by continued fraction representation
  • Gauss–Kuzmin–Wirsing operator
  • Lochs theorem
  • Minkowskis question mark function
  • Levys constant
  • Gelfond–Schneider constant
  • Thue–Siegel–Roth theorem
  • Equidistribution mod 1
  • Beattys theorem
  • Kroneckers theorem
  • Littlewood conjecture
  • Illustration of a low-discrepancy sequence
  • Constructions of low-discrepancy sequences
  • Prouhet–Thue–Morse constant
  • Discrepancy function
  • Halton sequences
  • Low-discrepancy sequence
  • Picks theorem
  • Minkowskis theorem
  • Mahlers compactness theorem
  • Geometry of numbers
  • Effective results in number theory
  • Mahlers theorem
  • Mahler measure


                                     

8. Sieve methods

  • Sieve of Atkin
  • Larger sieve
  • Function field sieve
  • Turan sieve
  • General number field sieve
  • Quadratic sieve
  • Sieve of Sundaram
  • Large sieve
  • Brun sieve
  • Selberg sieve
  • Sieve of Eratosthenes
                                     

9. Named primes

  • Mersenne prime
  • New Mersenne conjecture
  • Chen prime
  • Cullen prime
  • Fermat prime
  • Great Internet Mersenne Prime Search
  • Sophie Germain prime, safe prime
  • Wieferich prime
  • Wilson prime
  • Woodall prime
  • Prime pages
  • Wagstaff prime
  • Newman–Shanks–Williams prime
  • Wolstenholme prime
  • Primorial prime
  • Wall–Sun–Sun prime
                                     

10. Combinatorial number theory

  • Polynomial method
  • Covering system
  • Van der Waerdens theorem
  • Szemeredis theorem
  • Erdos–Ginzburg–Ziv theorem
  • Erdos–Graham conjecture
  • Gilbreaths conjecture
  • Collatz conjecture
  • Znams problem
  • Small set combinatorics
                                     

11.1. Computational number theory Primality tests

  • Probabilistic algorithm
  • Euler pseudoprime
  • Probable prime
  • Trial division
  • Fermat primality test
  • Carmichael number
  • Prime factorization algorithm
  • Pseudoprime
  • Fibonacci pseudoprime
  • Sieve of Eratosthenes
  • Euler–Jacobi pseudoprime
  • Miller–Rabin primality test
  • NewPGen
  • Baillie-PSW primality test
  • Lucas–Lehmer primality test
  • AKS primality test
  • Lucas–Lehmer test for Mersenne numbers
                                     

11.2. Computational number theory Integer factorization

  • General number field sieve
  • Pollards p − 1 algorithm
  • Special number field sieve
  • RSA Factoring Challenge
  • Pollards rho algorithm
  • Shors algorithm
  • Lenstra elliptic curve factorization
  • Quadratic sieve


                                     

11.3. Computational number theory Pseudo-random numbers

  • Pseudorandom number generator
  • Cryptographically secure pseudo-random number generator
  • Pseudorandomness
  • ACORN
  • Linear feedback shift register
  • Shrinking generator
  • Stream cipher
  • Lagged Fibonacci generator
  • ISAAC
  • Blum Shub
  • Linear congruential generator
  • Middle-square method
  • Mersenne twister

see also List of random number generators.

                                     

12. Arithmetic dynamics

  • Betrothed numbers
  • Perfect number
  • Sociable number
  • Aliquot sequence and Aliquot sum dynamics
  • Deficient number
  • Amicable number
  • Almost perfect number
  • Quasiperfect number
  • Abundant number
  • Digit sum dynamics
  • Digital root
  • Collatz conjecture
  • Additive persistence
  • Multiplicative digital root
  • Digit product dynamics
  • Multiplicative persistence
  • Happy number
  • Lychrel number
  • Perfect digital invariant
                                     
  • list of recreational number theory topics see number theory recreational mathematics Listing here is not pejorative: many famous topics in number
  • This is a list of algebraic number theory topics These topics are basic to the field, either as prototypical examples, or as basic objects of study. Algebraic
  • algebra topics List of homological algebra topics List of group theory topics List of representation theory topics List of linear algebra topics List of reciprocity
  • foundational results. analytic number theory areas of mathematics list of number theory topics list of probability topics probabilistic method probable
  • a list of articles related to set theory Algebra of sets Axiom of choice Axiom of countable choice Axiom of dependent choice Zorn s lemma Axiom of power
  • 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
  • Sylow J. Thompson J. Tits Helmut Wielandt H. Zassenhaus M. Zorn List of abstract algebra topics List of category theory topics List of Lie group topics
  • This is a list of graph theory topics by Wikipedia page. See glossary of graph theory terms for basic terminology Amalgamation Bipartite graph Complete
  • a list of mathematical topics in quantum theory by Wikipedia page. See also list of functional analysis topics list of Lie group topics list of quantum - mechanical
  • or precedes another. An alphabetical list of many notions of order theory can be found in the order theory glossary. See also inequality, extreme value
  • This is a list of computability and complexity topics by Wikipedia page. Computability theory is the part of the theory of computation that deals with