External resources

• Number theory by Internet Encyclopedia of Science
• Number theory by Wikipedia

Concepts

• Abc conjecture
• Abelian variety of CM-type
• Abel's summation formula
• Abouabdillah's theorem
• Abundant number
• Achilles number
• Algebraic number
• Almost perfect number
• Almost prime
• Alternating factorial
• Amenable number
• Amicable number
• Analytic number theory
• Antichain
• Arithmetic derivative
• Arithmetic hyperbolic 3-manifold
• Arithmetic progression
• Arithmetic variety
• Artin-Hasse exponential
• Aurifeuillian factorization
• Automorphic form
• Auxiliary function
• Ax-Kochen theorem
• Ban number
• Barnes G-function
• Basel problem
• Beal's conjecture
• Beatty sequence
• Beaver bit-vector decision procedure
• Bell number
• Bernoulli number
• Bernoulli polynomials
• Bertrand's postulate
• Binomial coefficient
• Birch and Swinnerton-Dyer conjecture
• Blum integer
• Bonse's inequality
• Brocard's problem
• Büchi's Problem
• Cabtaxi number
• Calkin-Wilf tree
• Carmichael number
• Carol number
• Catalan number
• Catalan's conjecture
• Champernowne constant
• Change-making problem
• Character group
• Chowla-Selberg formula
• Coin problem
• Collatz conjecture
• Colossally abundant number
• Complete sequence
• Composite number
• Computational number theory
• Congruent number
• Congruum
• Coprime
• Covering set
• Covering system
• Cryptography
• Cullen number
• Cunningham number
• Cunningham project
• Cyclic number
• Cyclotomic polynomial
• Dedekind number
• Dedekind sum
• Deficient number
• Delannoy number
• De Polignac's formula
• Digital root
• Digit sum
• Diophantine approximation
• Dirichlet convolution
• Divisibility sequence
• Divisor function
• Double Mersenne number
• Ducci sequence
• Durfee square
• E-function
• Egyptian fraction
• Eisenstein's theorem
• Elkies trinomial curves
• Elliptic divisibility sequence
• Equidigital number
• Erdős arcsine law
• Erdős-Fuchs theorem
• Erdős-Graham problem
• Erdős-Kac theorem
• Erdős-Woods number
• Eta function
• Euclid-Mullin sequence
• Euclid number
• Euclid's lemma
• Euler function
• Eulerian number
• Euler product
• Euler's rule
• Euler's sum of powers conjecture
• Euler's totient function
• Exponential factorial
• Extravagant number
• Factorial
• Factorial prime
• Factorion
• Faltings' theorem
• Farey sequence
• Feit-Thompson conjecture
• Fermat-Catalan conjecture
• Fermat number
• Fermat quotient
• Fermat's Last Theorem
• Figurate number
• Formulas for generating Pythagorean triples
• Fortunate number
• Fourth power
• Fractal sequence
• Friendly number
• Frugal number
• Fundamental theorem of arithmetic
• Generalized taxicab number
• Genocchi number
• Giuga number
• Glaisher-Kinkelin constant
• Golomb ruler
• Golomb sequence
• Goormaghtigh conjecture
• Granville number
• Greedy algorithm for Egyptian fractions
• Grothendieck-Katz p-curvature conjecture
• Haran's diamond theorem
• Harmonic divisor number
• Harmonic number
• Hasse-Minkowski theorem
• Hasse's theorem on elliptic curves
• Hecke character
• Height of a polynomial
• Hermite number
• Highly abundant number
• Highly composite number
• Highly cototient number
• Highly totient number
• Hilbert number
• Hilbert's irreducibility theorem
• Hofstadter sequence
• Holonomic constant
• Home prime
• Hyperperfect number
• Ideal lattice cryptography
• Idoneal number
• Integer square root
• Integer-valued polynomial
• Interprime
• Jacobi-Madden equation
• Jacobi's four-square theorem
• Jacobsthal number
• Jordan's totient function
• Juggler sequence
• Knödel number
• Krasner's lemma
• Kynea number
• Lah number
• Lambek-Moser theorem
• Landsberg-Schaar relation
• Langlands program
• Lazy caterer's sequence
• Legendre relation
• Lehmer number
• Lehmer's conjecture
• Leonardo number
• Leyland number
• Lindemann-Weierstrass theorem
• Linear congruence theorem
• Linear forms in logarithms
• List of mathematical functions
• List of types of functions
• Lobb numbers
• Local analysis
• Lonely runner conjecture
• Lucas-Carmichael number
• Lucas chain
• Lucas number
• Lucas sequence
• Lucas' theorem
• Lucky number
• Lucky numbers of Euler
• Lychrel number
• Magic constant
• Marshall Hall's conjecture
• Meertens number
• Mersenne number
• Mersenne prime
• Mertens conjecture
• Mian-Chowla sequence
• Mirimanoff's congruence
• Möbius transform
• Morton number
• Motzkin number
• MRB constant
• Multiplicative digital root
• Multiplicative partition
• Multiply perfect number
• Natural density
• Néron model
• Néron-Tate height
• Niven's constant
• Noncototient
• Nonhypotenuse number
• Nontotient
• Normal number
• Number Theory Foundation
• Numerical semigroup
• Ostrowski's theorem
• Overconvergent modular form
• P-adic analysis
• P-adic number
• P-adic order
• Padovan sequence
• Pairwise coprime
• Paley graph
• Pell number
• Pentagonal number theorem
• Perfect digit-to-digit invariant
• Perfect number
• Perfect power
• Perfect totient number
• Perrin number
• Persistence of a number
• Polite number
• Poly-Bernoulli number
• Postage stamp problem
• Poussin proof
• Powerful number
• Primary pseudoperfect number
• Primefree sequence
• Prime number
• Prime signature
• Primitive abundant number
• Primitive permutation group
• Primitive semiperfect number
• Primorial
• Primorial prime
• Probabilistic number theory
• Pronic number
• Proof of Fermat's Last Theorem for specific exponents
• Proof of weak Scholz conjecture
• Proofs of Fermat's little theorem
• Prosolvable group
• Proth number
• Prouhet-Tarry-Escott problem
• Prouhet-Thue-Morse constant
• Q-analog
• Q-derivative
• Q-Pochhammer symbol
• Quadratic integer
• Quadratic irrational
• Quadratic reciprocity
• Quartic reciprocity
• Quasiperfect number
• Quote notation
• Q-Vandermonde identity
• Radical of an integer
• Ramanujan's congruences
• Ramanujan's sum
• Random Fibonacci sequence
• Random partition
• Real numbers
• Refactorable number
• Regular number
• Residue class-wise affine group
• Rough number
• Schanuel's conjecture
• Schnorr group
• Schoof-Elkies-Atkin algorithm
• Schoof's algorithm
• Schröder number
• Schwartz-Bruhat function
• Semiperfect number
• Semiprime
• Semistable abelian variety
• Sidon sequence
• Sierpinski number
• Singly and doubly even
• Singmaster's conjecture
• Skew binary number system
• Skewes' number
• Smarandache function
• Smooth number
• Sociable number
• Somos sequence
• Sophie Germain's theorem
• Sparsely totient number
• Sparse ruler
• Sphenic number
• Spt function
• Squared triangular number
• Square-free integer
• Square triangular number
• Stern-Brocot tree
• Stern's diatomic series
• Stirling number
• Stoneham number
• Størmer number
• Størmer's theorem
• Strict differentiability
• Strictly non-palindromic number
• Strict weak ordering
• Sublime number
• Sum-free sequence
• Superabundant number
• Superior highly composite number
• Supernatural numbers
• Superperfect number
• Super-Poulet number
• Sylvester's sequence
• Szpiro's conjecture
• Tate's algorithm
• Tate twist
• Taxicab number
• Thâbit ibn Kurrah rule
• Thabit number
• Theta function of a lattice
• Tijdeman's theorem
• Triangular number
• Tunnell's theorem
• Turán-Kubilius inequality
• Ulam number
• Unitary divisor
• Unitary perfect number
• Untouchable number
• Unusual number
• Vieta jumping
• Vinogradov's theorem
• Von Staudt-Clausen theorem
• Vorlesungen über Zahlentheorie
• Wedderburn-Etherington number
• Weil-Châtelet group
• Weird number
• Wiener-Ikehara theorem
• Wiles' proof of Fermat's Last Theorem
• Wilson quotient
• Woodall number
• Zeckendorf's theorem
• Zeisel number
• Znám's problem
• Zolotarev's lemma
• Zsigmondy's theorem

Synonyms