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Additive Number Theory—Wolfram Language Documentation

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• Functions
  • DigitSum
  • DirichletConvolve
  • DiscreteConvolve
  • DivisorSigma
  • DivisorSum
  • EulerPhi
  • FrobeniusNumber
  • FrobeniusSolve
  • IntegerDigits
  • IntegerPartitions
  • MixedRadix
  • Mod
  • MoebiusMu
  • NumberDecompose
  • PartitionsP
  • PartitionsQ
  • PowersRepresentations
  • PrimeNu
  • PrimeOmega
  • Product
  • Reduce
  • Solve
  • SquaresR
  • Sum
• Related Guides
  • Multiplicative Number Theory
  • General Number Theory
  • Diophantine Equations
• Tech Notes
  • Solving Frobenius Equations and Computing Frobenius Numbers

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

IntegerPartitions — find restricted and unrestricted partitions of integers

PartitionsP  ▪  PartitionsQ

IntegerDigits  ▪  MixedRadix  ▪  NumberDecompose

PowersRepresentations — find representations of integers as sums of powers

SquaresR  ▪  FrobeniusNumber  ▪  FrobeniusSolve  ▪  Reduce  ▪  Solve

Sum, Product — general symbolic sums and products

DirichletConvolve  ▪  DivisorSum  ▪  DigitSum  ▪  DiscreteConvolve

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

Mod  ▪  EulerPhi  ▪  MoebiusMu  ▪  DivisorSigma  ▪  ...

▪
• Solving Frobenius Equations and Computing Frobenius Numbers

▪
• Multiplicative Number Theory
▪
• General Number Theory
▪
• Diophantine Equations

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