Functions and mappings | Modular arithmetic

Carmichael function

In number theory, a branch of mathematics, the Carmichael function λ(n) of a positive integer n is the smallest positive integer m such that holds for every integer a coprime to n. In algebraic terms, λ(n) is the exponent of the multiplicative group of integers modulo n. The Carmichael function is named after the American mathematician Robert Carmichael who defined it in 1910. It is also known as Carmichael's λ function, the reduced totient function, and the least universal exponent function. The following table compares the first 36 values of λ(n) (sequence in the OEIS) with Euler's totient function φ (in bold if they are different; the ns such that they are different are listed in OEIS: ). (Wikipedia).

Carmichael function
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Related pages

Square-free integer | Multiplicative order | Euler's theorem | Chinese remainder theorem | Least common multiple | Euler's totient function | Mathematics | Multiplicative group of integers modulo n | Number theory | Integer | Primitive root modulo n | RSA (cryptosystem) | Unit (ring theory) | Group theory | Cryptography | Finite group | Carmichael number | Robert Daniel Carmichael