gives the Carmichael function .
- CarmichaelLambda is also known as the reduced totient function or the least universal exponent function.
- CarmichaelLambda is typically used in primality testing to find a composite number that cannot be proved composite by some primality tests.
- Integer mathematical function, suitable for both symbolic and numerical manipulation.
- CarmichaelLambda[n] is the smallest positive integer such that for all relatively prime to .
- For a number with a unit and primes, CarmichaelLambda[n] returns LCM[(p1-1),…,(pm-1)].
Examplesopen allclose all
Basic Examples (2)
Compute CarmichaelLambda of :
Basic Applications (3)
The first 20 values of CarmichaelLambda:
Primality Testing (2)
Properties & Relations (7)
The multiplicative order of an element modulo divides CarmichaelLambda[n]:
Wolfram Research (1999), CarmichaelLambda, Wolfram Language function, https://reference.wolfram.com/language/ref/CarmichaelLambda.html (updated 2018).
Wolfram Language. 1999. "CarmichaelLambda." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2018. https://reference.wolfram.com/language/ref/CarmichaelLambda.html.
Wolfram Language. (1999). CarmichaelLambda. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CarmichaelLambda.html