Samiksha Jaiswal (Editor)

List of number theory topics

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This is a list of number theory topics, by Wikipedia page. See also

Contents

  • List of recreational number theory topics
  • Topics in cryptography
  • Factors

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

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

  • Montgomery reduction
  • Modular exponentiation
  • Linear congruence theorem
  • Method of successive substitution
  • Chinese remainder theorem
  • Fermat's little theorem
  • Proofs of Fermat's little theorem
  • Fermat quotient
  • Euler's totient function
  • Noncototient
  • Nontotient
  • Euler's theorem
  • Wilson's theorem
  • Primitive root modulo n
  • Multiplicative order
  • Discrete logarithm
  • Quadratic residue
  • Euler's criterion
  • Legendre symbol
  • Gauss's lemma (number theory)
  • Congruence of squares
  • Luhn formula
  • Mod n cryptanalysis
  • Arithmetic functions

  • Multiplicative function
  • Additive function
  • Dirichlet convolution
  • Erdős–Kac theorem
  • Möbius function
  • Möbius inversion formula
  • Divisor function
  • Liouville function
  • Partition function (number theory)
  • Integer partition
  • Bell numbers
  • Landau's function
  • Pentagonal number theorem
  • Bell series
  • Lambert series
  • Analytic number theory: additive problems

  • Twin prime
  • Brun's constant
  • Cousin prime
  • Prime triplet
  • Prime quadruplet
  • Sexy prime
  • Sophie Germain prime
  • Cunningham chain
  • Goldbach's conjecture
  • Goldbach's weak conjecture
  • Second Hardy–Littlewood conjecture
  • Hardy–Littlewood circle method
  • Schinzel's hypothesis H
  • Bateman–Horn conjecture
  • Waring's problem
  • Brahmagupta–Fibonacci identity
  • Euler's four-square identity
  • Lagrange's four-square theorem
  • Taxicab number
  • Generalized taxicab number
  • Cabtaxi number
  • Schnirelmann density
  • Sumset
  • Landau–Ramanujan constant
  • Sierpinski number
  • Seventeen or Bust
  • Niven's constant
  • Algebraic number theory

    See list of algebraic number theory topics

    Quadratic forms

  • Unimodular lattice
  • Fermat's theorem on sums of two squares
  • Proofs of Fermat's theorem on sums of two squares
  • L-functions

  • Riemann zeta function
  • Basel problem on ζ(2)
  • Hurwitz zeta function
  • Bernoulli number
  • Agoh–Giuga conjecture
  • Von Staudt–Clausen theorem
  • Dirichlet series
  • Euler product
  • Prime number theorem
  • Prime-counting function
  • Meissel–Lehmer algorithm
  • Offset logarithmic integral
  • Legendre's constant
  • Skewes' number
  • Bertrand's postulate
  • Proof of Bertrand's postulate
  • Proof that the sum of the reciprocals of the primes diverges
  • Cramér's conjecture
  • Riemann hypothesis
  • Critical line theorem
  • Hilbert–Pólya conjecture
  • Generalized Riemann hypothesis
  • Mertens function, Mertens conjecture, Meissel–Mertens constant
  • De Bruijn–Newman constant
  • Dirichlet character
  • Dirichlet L-series
  • Siegel zero
  • Dirichlet's theorem on arithmetic progressions
  • Linnik's theorem
  • Elliott–Halberstam conjecture
  • Functional equation (L-function)
  • Chebotarev's density theorem
  • Local zeta function
  • Weil conjectures
  • Modular form
  • modular group
  • Congruence subgroup
  • Hecke operator
  • Cusp form
  • Eisenstein series
  • Modular curve
  • Ramanujan–Petersson conjecture
  • Birch and Swinnerton-Dyer conjecture
  • Automorphic form
  • Selberg trace formula
  • Artin conjecture
  • Sato–Tate conjecture
  • Langlands program
  • modularity theorem
  • Diophantine equations

  • Pythagorean triple
  • Pell's equation
  • Elliptic curve
  • Nagell–Lutz theorem
  • Mordell–Weil theorem
  • Mazur's torsion theorem
  • Congruent number
  • Arithmetic of abelian varieties
  • Elliptic divisibility sequences
  • Mordell curve
  • Fermat's Last Theorem
  • Mordell conjecture
  • Euler's sum of powers conjecture
  • abc Conjecture
  • Catalan's conjecture
  • Pillai's conjecture
  • Hasse principle
  • Diophantine set
  • Matiyasevich's theorem
  • Hundred Fowls Problem
  • 1729
  • Diophantine approximation

  • Davenport–Schmidt theorem
  • Irrational number
  • Square root of two
  • Quadratic irrational
  • Integer square root
  • Algebraic number
  • Pisot–Vijayaraghavan number
  • Salem number
  • Transcendental number
  • e (mathematical constant)
  • pi, list of topics related to pi
  • Squaring the circle
  • Proof that e is irrational
  • Lindemann–Weierstrass theorem
  • Hilbert's seventh problem
  • Gelfond–Schneider theorem
  • Erdős–Borwein constant
  • Liouville number
  • Continued fraction
  • Mathematical constant (sorted by continued fraction representation)
  • Khinchin's constant
  • Lévy's constant
  • Lochs' theorem
  • Gauss–Kuzmin–Wirsing operator
  • Minkowski's question mark function
  • Generalized continued fraction
  • Kronecker's theorem
  • Thue–Siegel–Roth theorem
  • Prouhet–Thue–Morse constant
  • Gelfond–Schneider constant
  • Equidistribution mod 1
  • Beatty's theorem
  • Littlewood conjecture
  • Discrepancy function
  • Low-discrepancy sequence
  • Illustration of a low-discrepancy sequence
  • Constructions of low-discrepancy sequences
  • Halton sequences
  • Geometry of numbers
  • Minkowski's theorem
  • Pick's theorem
  • Mahler's compactness theorem
  • Mahler measure
  • Effective results in number theory
  • Mahler's theorem
  • Sieve methods

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

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

  • Covering system
  • Small set (combinatorics)
  • Erdős–Ginzburg–Ziv theorem
  • Polynomial method
  • Van der Waerden's theorem
  • Szemerédi's theorem
  • Collatz conjecture
  • Gilbreath's conjecture
  • Erdős–Graham conjecture
  • Znám's problem
  • Computational number theory

    Note: Computational number theory is also known as algorithmic number theory.

  • Residue number system
  • Cunningham project
  • Quadratic residuosity problem
  • Primality tests

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

  • Pollard's p − 1 algorithm
  • Pollard's rho algorithm
  • Lenstra elliptic curve factorization
  • Quadratic sieve
  • Special number field sieve
  • General number field sieve
  • Shor's algorithm
  • RSA Factoring Challenge
  • Pseudo-random numbers

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

  • Disquisitiones Arithmeticae
  • "On the Number of Primes Less Than a Given Magnitude"
  • Vorlesungen über Zahlentheorie
  • Prime Obsession
  • References

    List of number theory topics Wikipedia


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