FrobeniusSolve

FrobeniusSolve[{a1,,an},b]

gives a list of all solutions of the Frobenius equation .

FrobeniusSolve[{a1,,an},b,m]

gives at most m solutions.

Details

  • The Frobenius equation is the Diophantine equation , where the ai are positive integers, b is an integer, and a solution must consist of non-negative integers. For negative b there are no solutions.

Examples

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Basic Examples  (1)

All solutions of the Frobenius equation :

Check:

Properties & Relations  (2)

Reduce may also be used to find the solutions to the Frobenius equation:

FrobeniusSolve returns the same solution set:

FrobeniusSolve gives coefficient lists for IntegerPartitions:

Introduced in 2007
 (6.0)