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Integer Functions
Mathematica contains hundreds of original algorithms for computing integer functions involving integers of any size.
Division-Related Functions
Mod  ▪ PowerMod  ▪ Quotient  ▪ QuotientRemainder  ▪ GCD  ▪ LCM  ▪ Divisible  ▪ CoprimeQ  ▪ EvenQ  ▪ OddQ  ▪ PrimeQ
Combinatorial Functions »
Factorial(!)  ▪ Binomial  ▪ Multinomial  ▪ CatalanNumber  ▪ StirlingS1  ▪ PartitionsP  ▪ BellB  ▪ FrobeniusNumber  ▪ ...
Recurrence and Sum Functions »
Fibonacci  ▪ LucasL  ▪ HarmonicNumber  ▪ BernoulliB  ▪ EulerE  ▪ MatrixExp  ▪ ...
Integer Decompositions
FactorInteger  ▪ Divisors  ▪ IntegerPartitions  ▪ IntegerDigits  ▪ FrobeniusSolve
Digit-Related Functions »
IntegerDigits  ▪ FromDigits  ▪ IntegerLength  ▪ DigitCount  ▪ IntegerExponent  ▪ ...
Bitwise Functions »
BitAnd  ▪ BitOr  ▪ BitXor  ▪ BitLength  ▪ BitShiftLeft  ▪ BitSet  ▪ ...
    
RSolve — solve integer recurrences
Sum — find sums of integer functions
FindSequenceFunction — find functional forms from sequences
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