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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 n^(th) prime
PrimeQ — test for primality
NextPrime  ▪ PrimePi  ▪ PrimeOmega  ▪ 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  ▪ DivisorSum  ▪ DedekindEta  ▪ EllipticTheta  ▪ ...
Partitions »
IntegerPartitions  ▪ PartitionsP  ▪ StirlingS1  ▪ StirlingS2  ▪ FrobeniusNumber  ▪
Representations as Sums of Powers
SquaresR  ▪ PowersRepresentations  ▪ EllipticTheta
Digit Representations »
IntegerDigits  ▪ FromDigits  ▪ DigitCount  ▪ IntegerExponent  ▪ Log2  ▪ ...
    
Multiplicative Number Theory »
MoebiusMu  ▪ EulerPhi  ▪ DivisorSigma  ▪ MangoldtLambda  ▪ PrimeNu  ▪ ...
Analytic Number Theory »
Zeta  ▪ ZetaZero  ▪ RiemannSiegelZ  ▪ LerchPhi  ▪ DirichletL  ▪ RamanujanTau  ▪ ...
Additive Number Theory »
PartitionsP  ▪ PartitionsQ  ▪ BellB  ▪ SquaresR  ▪ ...
Algebraic Number Theory »
AlgebraicNumberNorm  ▪ NumberFieldDiscriminant  ▪ ...
TUTORIALS
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