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