PowersRepresentations

PowersRepresentations[n,k,p]

gives the distinct representations of the integer n as a sum of k non-negative p^(th) integer powers.

Details

Examples

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Basic Examples  (1)

Find representations of 1729 as a sum of two cubes:

Scope  (2)

Representation of relatively large numbers as the sum of two squares:

Known taxicab numbers:

Properties & Relations  (2)

Use FindInstance to find a solution instance:

PowersRepresentations gives ordered partitions of fixed length:

Possible Issues  (1)

The scale of the computation increases rapidly with the size of the number:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_powersrepresentations, author="Wolfram Research", title="{PowersRepresentations}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/PowersRepresentations.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_powersrepresentations, organization={Wolfram Research}, title={PowersRepresentations}, year={2007}, url={https://reference.wolfram.com/language/ref/PowersRepresentations.html}, note=[Accessed: 22-December-2024 ]}