# 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:

Wolfram Research (2007), FrobeniusSolve, Wolfram Language function, https://reference.wolfram.com/language/ref/FrobeniusSolve.html.

#### Text

Wolfram Research (2007), FrobeniusSolve, Wolfram Language function, https://reference.wolfram.com/language/ref/FrobeniusSolve.html.

#### CMS

Wolfram Language. 2007. "FrobeniusSolve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FrobeniusSolve.html.

#### APA

Wolfram Language. (2007). FrobeniusSolve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FrobeniusSolve.html

#### BibTeX

@misc{reference.wolfram_2024_frobeniussolve, author="Wolfram Research", title="{FrobeniusSolve}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/FrobeniusSolve.html}", note=[Accessed: 13-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_frobeniussolve, organization={Wolfram Research}, title={FrobeniusSolve}, year={2007}, url={https://reference.wolfram.com/language/ref/FrobeniusSolve.html}, note=[Accessed: 13-July-2024 ]}