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Built-in Mathematica Symbol

CarmichaelLambda

CarmichaelLambda[n]
gives the Carmichael function

, defined as the smallest integer m such that

for all k relatively prime to n.

Integer mathematical function, suitable for both symbolic and numerical manipulation.

The first ten values of CarmichaelLambda:

Plot the sequence:

The first ten values of CarmichaelLambda:

Plot the sequence:

Evaluate for moderately large integers:

CarmichaelLambda threads element-wise over lists:

CarmichaelLambda works for negative integers:

Find Carmichael numbers [more info]:

Find their factorization:

Find integers k such that

Build RSA-like toy 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:

Model the Carmichael function based on the definition [more info]:

Check Carmichael's theorem [more info]:

Use FullSimplify to simplify expressions containing CarmichaelLambda:

Curious property of CarmichaelLambda: