IntegerPartitions[n] gives a list of all possible ways to partition the integer n into smaller integers. IntegerPartitions[n, k] gives partitions into at most k integers. ...

DiscreteMath`IntegerPartitions` was available as an add-on package in previous versions of Mathematica and is now available on the web at ...

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

Although Diophantine equations provide classic examples of undecidability, Mathematica in practice succeeds in solving a remarkably wide range of such equations—automatically ...

DiscreteMath`CombinatorialFunctions`, DiscreteMath`Combinatorica`, DiscreteMath`ComputationalGeometry`, DiscreteMath`GraphPlot`, DiscreteMath`IntegerPartitions`, ...

FrobeniusSolve[{a_1, ..., a_n}, b] gives a list of all solutions of the Frobenius equation a_1 x_1 + ... + a_n x_n = b. FrobeniusSolve[{a_1, ..., a_n}, b, m] gives at most m ...

PowersRepresentations[n, k, p] gives the distinct representations of the integer n as a sum of k non-negative p\[Null]^th integer powers. FPowersRepresentations[n, {a_1, a_2, ...

PartitionsQ[n] gives the number q (n) of partitions of the integer n into distinct parts.

New Combinatorial & Recurrence Functions, Subfactorial, CatalanNumber, LucasL, BellB, NorlundB, New Divisibility-Related Functions, Divisible, QuotientRemainder, CoprimeQ, ...

PartitionsP[n] gives the number p (n) of unrestricted partitions of the integer n.