PrimitiveRootList

PrimitiveRootList[n]

gives a list of primitive roots of n.

Details

  • A primitive root is a generator for the multiplicative group of integers modulo n relatively prime to n.
  • PrimitiveRootList[n] returns an empty list if n is not 2,4, an odd prime power, or twice an odd prime power.

Examples

Basic Examples  (1)

List of primitive roots of 9:

Primitive roots generate all integers modulo 9 that are relatively prime to 9:

Wolfram Research (2014), PrimitiveRootList, Wolfram Language function, https://reference.wolfram.com/language/ref/PrimitiveRootList.html.

Text

Wolfram Research (2014), PrimitiveRootList, Wolfram Language function, https://reference.wolfram.com/language/ref/PrimitiveRootList.html.

CMS

Wolfram Language. 2014. "PrimitiveRootList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PrimitiveRootList.html.

APA

Wolfram Language. (2014). PrimitiveRootList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PrimitiveRootList.html

BibTeX

@misc{reference.wolfram_2025_primitiverootlist, author="Wolfram Research", title="{PrimitiveRootList}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/PrimitiveRootList.html}", note=[Accessed: 02-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_primitiverootlist, organization={Wolfram Research}, title={PrimitiveRootList}, year={2014}, url={https://reference.wolfram.com/language/ref/PrimitiveRootList.html}, note=[Accessed: 02-March-2025 ]}