Carmichael function

Target entity: Carmichael function
Context triple: [Carmichael number, relatedConcept, Carmichael function]

• A. Euler’s totient function φ(n)
  Euler’s totient function φ(n) is a fundamental arithmetic function in number theory that counts the positive integers up to n that are relatively prime to n and plays a key role in topics such as modular arithmetic and cryptography.
• B. Carmichael number
  A Carmichael number is a composite integer that nonetheless satisfies Fermat's primality test for all bases coprime to it, making it a classic example of a Fermat pseudoprime.
• C. Möbius function
  The Möbius function is a multiplicative arithmetic function in number theory that assigns values based on the prime factorization of integers and plays a central role in inversion formulas and the study of prime distribution.
• D. Liouville function
  The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
• E. Mertens function
  The Mertens function is an arithmetic function in number theory defined as the cumulative sum of the Möbius function, playing a key role in the study of the distribution of prime numbers and the Riemann Hypothesis.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Carmichael function
Target entity description: The Carmichael function is a number-theoretic function that gives the smallest positive integer m such that a^m ≡ 1 (mod n) for all integers a coprime to n, playing a key role in modular arithmetic and cryptography.

• A. Euler’s totient function φ(n)
  Euler’s totient function φ(n) is a fundamental arithmetic function in number theory that counts the positive integers up to n that are relatively prime to n and plays a key role in topics such as modular arithmetic and cryptography.
• B. Carmichael number
  A Carmichael number is a composite integer that nonetheless satisfies Fermat's primality test for all bases coprime to it, making it a classic example of a Fermat pseudoprime.
• C. Möbius function
  The Möbius function is a multiplicative arithmetic function in number theory that assigns values based on the prime factorization of integers and plays a central role in inversion formulas and the study of prime distribution.
• D. Liouville function
  The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
• E. Mertens function
  The Mertens function is an arithmetic function in number theory defined as the cumulative sum of the Möbius function, playing a key role in the study of the distribution of prime numbers and the Riemann Hypothesis.
• F. None of above. chosen