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FrobeniusSolve
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FrobeniusSolve

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FrobeniusSolve[{a1,…,an},b]

gives a list of all solutions of the Frobenius equation .

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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)Summary of the most common use cases

All solutions of the Frobenius equation :

In[1]:=1
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https://wolfram.com/xid/0tp7rsbqdmfb9u-wte
Out[1]=1

Check:

In[2]:=2
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https://wolfram.com/xid/0tp7rsbqdmfb9u-raw
Out[2]=2

Scope  (1)Survey of the scope of standard use cases

Show that 43 cannot be represented as a sum of positive integer multiples of 6, 9 and 20:

In[2]:=2
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https://wolfram.com/xid/0tp7rsbqdmfb9u-1ubhqy
Out[2]=2

Find all such representations of 44:

In[1]:=1
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https://wolfram.com/xid/0tp7rsbqdmfb9u-uce0ke
Out[1]=1

Return just a single representation:

In[1]:=1
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https://wolfram.com/xid/0tp7rsbqdmfb9u-hh1fs
Out[1]=1

Properties & Relations  (2)Properties of the function, and connections to other functions

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

In[1]:=1
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https://wolfram.com/xid/0tp7rsbqdmfb9u-q65
Out[1]=1

FrobeniusSolve returns the same solution set:

In[2]:=2
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https://wolfram.com/xid/0tp7rsbqdmfb9u-g73
Out[2]=2

FrobeniusSolve gives coefficient lists for IntegerPartitions:

In[1]:=1
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https://wolfram.com/xid/0tp7rsbqdmfb9u-twrtg
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0tp7rsbqdmfb9u-iz73l8
Out[2]=2
Wolfram Research (2007), FrobeniusSolve, Wolfram Language function, https://reference.wolfram.com/language/ref/FrobeniusSolve.html.
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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.

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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.

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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

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

BibTeX

@misc{reference.wolfram_2025_frobeniussolve, author="Wolfram Research", title="{FrobeniusSolve}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/FrobeniusSolve.html}", note=[Accessed: 02-April-2025 ]}

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@misc{reference.wolfram_2025_frobeniussolve, author="Wolfram Research", title="{FrobeniusSolve}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/FrobeniusSolve.html}", note=[Accessed: 02-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_frobeniussolve, organization={Wolfram Research}, title={FrobeniusSolve}, year={2007}, url={https://reference.wolfram.com/language/ref/FrobeniusSolve.html}, note=[Accessed: 02-April-2025 ]}

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@online{reference.wolfram_2025_frobeniussolve, organization={Wolfram Research}, title={FrobeniusSolve}, year={2007}, url={https://reference.wolfram.com/language/ref/FrobeniusSolve.html}, note=[Accessed: 02-April-2025 ]}