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 ...

FrobeniusInstance and FrobeniusSolve are now available as the newly added built-in Mathematica kernel function FrobeniusSolve. FrobeniusF is now available as the newly added ...

Mathematica normally assumes that variables which appear in equations can stand for arbitrary complex numbers. But when you use Reduce, you can explicitly tell Mathematica ...

A Frobenius equation is an equation of the form where a_1, …, a_n are positive integers, m is an integer, and the coordinates x_1, …, x_n of solutions are required to be ...

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 ...

FrobeniusNumber[{a_1, ..., a_n}] gives the Frobenius number of a_1, ..., a_n.

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

Mathematica contains hundreds of original algorithms for computing integer functions involving integers of any size.

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. ...