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Mathematica > Mathematics and Algorithms > Mathematical Functions >
Number Theoretic Functions
Mathematica contains the world's largest collection of number theoretic functions, many based on specially developed algorithms.
Primes and their Distribution »
Prime — the nth prime
PrimeQ — test for primality
NextPrime  ▪ PrimePi  ▪ LogIntegral  ▪ Zeta  ▪ ZetaZero
Integer Factorization
FactorInteger — find the factors of an integer
SquareFreeQ  ▪ PrimePowerQ
Divisibility
GCD  ▪ LCM  ▪ Divisible  ▪ CoprimeQ  ▪ ExtendedGCD
EulerPhi  ▪ MoebiusMu  ▪ JacobiSymbol  ▪ KroneckerSymbol
Congruences
Mod  ▪ PowerMod  ▪ MultiplicativeOrder  ▪ PrimitiveRoot  ▪ ChineseRemainder  ▪ PowerModList  ▪ CarmichaelLambda
Divisors
Divisors  ▪ DivisorSigma  ▪ DedekindEta  ▪ EllipticTheta
Partitions
IntegerPartitions  ▪ PartitionsP  ▪ StirlingS1  ▪ StirlingS2  ▪ BellB  ▪ FrobeniusNumber
Representations as Sums of Powers
SquaresR  ▪ PowersRepresentations  ▪ EllipticTheta
Digit Representations »
IntegerDigits  ▪ FromDigits  ▪ DigitCount  ▪ IntegerExponent
Analytic Number Theory
Zeta  ▪ RiemannSiegelZ  ▪ RiemannSiegelTheta  ▪ LerchPhi
RamanujanTau  ▪ RamanujanTauL  ▪ RamanujanTauTheta  ▪ RamanujanTauZ
Algebraic Number Theory »
AlgebraicNumberNorm  ▪ NumberFieldDiscriminant  ▪ ...
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