List of number theory topics
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This is a list of number theory topics, by Wikipedia page. See also
Contents
Factors
- Composite number
- *Highly composite number
- Even and odd numbers
- *Parity
- Divisor, aliquot, aliquant
- *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
- Prime factor
- *Table of prime factors
- Formula for primes
- Factorization
- *RSA number
- Fundamental theorem of arithmetic
- Square-free
- Perfect square
- Power of two
- Integer-valued polynomial
- Clock arithmetic
- Advanced modular arithmetic theory
- Montgomery reduction
- Modular exponentiation
- Linear congruence theorem
- Method of successive substitution
- Chinese remainder theorem
- Fermat's little theorem
- *Proofs of Fermat's little theorem
- 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 lemma
- Congruence of squares
- Luhn formula
- Mod n cryptanalysis
- Twin prime
- *Twin prime conjecture
- *Brun's constant
- Cousin prime
- 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
See list of algebraic number theory topics
- 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
- *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-Polya 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
- *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
- Taniyama-Shimura theorem
- Pythagorean triple
- Pell's equation
- Elliptic curve
- *Nagell-Lutz theorem
- *Mordell-Weil theorem
- *Mazur's torsion theorem
- *Congruent number
- *Arithmetic of abelian varieties
- Fermat's last theorem
- Mordell conjecture
- Euler's conjecture
- abc Conjecture
- Catalan's conjecture
- Pillai's conjecture
- Hasse principle
- Diophantine set
- Matiyasevich's theorem
- One thousand seven hundred and twenty nine
- 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
- *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
Named primes
Combinatorial number theory
- Clock arithmetic
- Advanced modular arithmetic theory
- Montgomery reduction
- Modular exponentiation
- Linear congruence theorem
- Method of successive substitution
- Chinese remainder theorem
- Fermat's little theorem
- *Proofs of Fermat's little theorem
- 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 lemma
- Congruence of squares
- Luhn formula
- Mod n cryptanalysis
- Twin prime
- *Twin prime conjecture
- *Brun's constant
- Cousin prime
- 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
See list of algebraic number theory topics
- 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
- *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-Polya 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
- *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
- Taniyama-Shimura theorem
- Pythagorean triple
- Pell's equation
- Elliptic curve
- *Nagell-Lutz theorem
- *Mordell-Weil theorem
- *Mazur's torsion theorem
- *Congruent number
- *Arithmetic of abelian varieties
- Fermat's last theorem
- Mordell conjecture
- Euler's conjecture
- abc Conjecture
- Catalan's conjecture
- Pillai's conjecture
- Hasse principle
- Diophantine set
- Matiyasevich's theorem
- One thousand seven hundred and twenty nine
- 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
- *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
Named primes
Combinatorial number theory
- Twin prime
- *Twin prime conjecture
- *Brun's constant
- Cousin prime
- 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
See list of algebraic number theory topics
- 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
- *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-Polya 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
- *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
- Taniyama-Shimura theorem
- Pythagorean triple
- Pell's equation
- Elliptic curve
- *Nagell-Lutz theorem
- *Mordell-Weil theorem
- *Mazur's torsion theorem
- *Congruent number
- *Arithmetic of abelian varieties
- Fermat's last theorem
- Mordell conjecture
- Euler's conjecture
- abc Conjecture
- Catalan's conjecture
- Pillai's conjecture
- Hasse principle
- Diophantine set
- Matiyasevich's theorem
- One thousand seven hundred and twenty nine
- 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
- *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
Named primes
Combinatorial number theory
- 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
- *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-Polya 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
- *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
- Taniyama-Shimura theorem
- Pythagorean triple
- Pell's equation
- Elliptic curve
- *Nagell-Lutz theorem
- *Mordell-Weil theorem
- *Mazur's torsion theorem
- *Congruent number
- *Arithmetic of abelian varieties
- Fermat's last theorem
- Mordell conjecture
- Euler's conjecture
- abc Conjecture
- Catalan's conjecture
- Pillai's conjecture
- Hasse principle
- Diophantine set
- Matiyasevich's theorem
- One thousand seven hundred and twenty nine
- 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
- *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
Named primes
- Pythagorean triple
- Pell's equation
- Elliptic curve
- *Nagell-Lutz theorem
- *Mordell-Weil theorem
- *Mazur's torsion theorem
- *Congruent number
- *Arithmetic of abelian varieties
- Fermat's last theorem
- Mordell conjecture
- Euler's conjecture
- abc Conjecture
- Catalan's conjecture
- Pillai's conjecture
- Hasse principle
- Diophantine set
- Matiyasevich's theorem
- One thousand seven hundred and twenty nine
- 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
- *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
Named primes
Named primes
- Covering system
- Small set (combinatorics)
- Erdős-Ginzburg-Ziv theorem
- Polynomial method
- Van der Waerden's theorem
- Szemerédi's theorem
- Collatz conjecture
- Gilbreath's conjecture
- Znám's problem
- 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
- Miller-Rabin primality test
- Lucas-Lehmer primality test
- Lucas-Lehmer test for Mersenne numbers
- AKS primality test
- NewPGen
History
- 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
- Miller-Rabin primality test
- Lucas-Lehmer primality test
- Lucas-Lehmer test for Mersenne numbers
- AKS primality test
- NewPGen
History
History
- Disquisitiones Arithmeticae
- On the Number of Primes Less Than a Given Magnitude
- Vorlesungen über Zahlentheorie
- Prime Obsession
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