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CarmichaelLambda—Wolfram Language Documentation

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BUILT-IN SYMBOL Details Examplesopen allclose all Scope  (7) Symbolic Manipulation  (3)

Find an integer solution instance:

Simplify an expression:

Identify the CarmichaelLambda sequence:

Applications  (7) Basic Applications  (3)

The first 20 values of CarmichaelLambda:

Discrete plot:

Number line plot:

Plot the generating function:

Exponential generating function:

Dirichlet series:

Primality Testing  (2)

Given a prime, for all positive numbers a less than p:

A natural test for primality:

This test can be inconclusive for composite integers n satisfying :

Verify for all a coprime to 561:

Recognize Carmichael numbers, composite numbers with an≡1 mod n for all a coprime to n:

The number is a Carmichael number, is not:

Cryptography  (1)

Build RSA-like encryption scheme. Start with the modulus:

Find the universal exponent of the multiplication group modulo n:

Private key:

Public key:

Encrypt a message:

Decrypt it:

Number Theory  (1)

Find the number of elements in the largest subgroup of Z_n^*:

Properties & Relations  (7) Wolfram Research (1999), CarmichaelLambda, Wolfram Language function, https://reference.wolfram.com/language/ref/CarmichaelLambda.html (updated 2018). Text

Wolfram Research (1999), CarmichaelLambda, Wolfram Language function, https://reference.wolfram.com/language/ref/CarmichaelLambda.html (updated 2018).

CMS

Wolfram Language. 1999. "CarmichaelLambda." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2018. https://reference.wolfram.com/language/ref/CarmichaelLambda.html.

APA

Wolfram Language. (1999). CarmichaelLambda. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CarmichaelLambda.html

BibTeX

@misc{reference.wolfram_2025_carmichaellambda, author="Wolfram Research", title="{CarmichaelLambda}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/CarmichaelLambda.html}", note=[Accessed: 12-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_carmichaellambda, organization={Wolfram Research}, title={CarmichaelLambda}, year={2018}, url={https://reference.wolfram.com/language/ref/CarmichaelLambda.html}, note=[Accessed: 12-July-2025 ]}

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