Additive Number Theory

Building on its broad algorithmic and mathematical capabilities, Mathematica provides a unique level of highly general and efficient support for additive number theory.

ReferenceReference

Integer Partitions

IntegerPartitions find restricted and unrestricted partitions of integers

PartitionsP ▪ PartitionsQ

Representation in Terms of Powers

PowersRepresentations find representations of integers as sums of powers

SquaresR ▪ FrobeniusNumber ▪ FrobeniusSolve ▪ Reduce ▪ Solve

Summation-Related Operations

Sum, Product general symbolic sums and products

DirichletConvolve ▪ DivisorSum ▪ DiscreteConvolve

Arithmetic Functions »

PrimeOmega, PrimeNu number of distinct prime factors (with, without multiplicities)

Mod ▪ EulerPhi ▪ MoebiusMu ▪ DivisorSigma ▪ ...

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