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 a m ≡ 1 (...

the product of the first 120569 primes. Carmichael function (λ) Dedekind psi function (𝜓) Divisor function (σ) Duffin–Schaeffer conjecture Generalizations...

In number theory, a Carmichael number is a composite number ⁠ n {\displaystyle n} ⁠ which in modular arithmetic satisfies the congruence relation: b n...

functions Liouville function, λ(n) = (–1)Ω(n) Von Mangoldt function, Λ(n) = log p if n is a positive power of the prime p Carmichael function Logarithmic integral...

In mathematics, Carmichael's totient function conjecture concerns the multiplicity of values of Euler's totient function φ(n), which counts the number...

a_{k}\;\land \;n=a_{1}+a_{2}+\cdots +a_{k}\right\}\right|.} λ(n), the Carmichael function, is the smallest positive number such that a λ ( n ) ≡ 1 ( mod n...

although they are not primes), Carmichael's totient function conjecture, Carmichael's theorem, and the Carmichael function, all significant in number theory...

function, λ(τ), a highly symmetric holomorphic function on the complex upper half-plane Carmichael function, λ(n), in number theory and group theory Lambda...

Kwame Ture (/ˈkwɑːmeɪ ˈtʊəreɪ/; born Stokely Standiford Churchill Carmichael; June 29, 1941 – November 15, 1998) was an American activist who played a...

and q of n. Fermat's little theorem is also related to the Carmichael function and Carmichael's theorem, as well as to Lagrange's theorem in group theory...

}}(M)}\right){\bmod {M}}} , where λ {\displaystyle \lambda } is the Carmichael function. (Here we have λ ( M ) = λ ( p ⋅ q ) = lcm ⁡ ( p − 1 , q − 1 ) {\displaystyle...

factor of λ(49) = 42, where λ(n) is known as the Carmichael function. This follows from Carmichael's theorem which states that if n is a positive integer...

generates it. The order of a (mod n) also divides λ(n), a value of the Carmichael function, which is an even stronger statement than the divisibility of φ(n)...

density ecliptic longitude in astronomy the Liouville function in number theory the Carmichael function in number theory the empty string in formal grammar...

no primitive roots modulo 15. Indeed, λ(15) = 4, where λ is the Carmichael function. (sequence A002322 in the OEIS) Numbers n {\displaystyle n} that...

{\displaystyle \phi (x)=k} , where ϕ {\displaystyle \phi } is Euler's totient function, than any integer smaller than it. The first few highly totient numbers...

\lambda (n))=1} , where λ ( n ) {\displaystyle \lambda (n)} is the Carmichael function. Compute d := e − 1 mod λ ( n ) {\displaystyle d:=e^{-1}{\bmod {\lambda...

≡ 1 (mod λ(N)), where λ(N) denotes the Carmichael function, though sometimes φ(N), the Euler's totient function, is used (note: this is the order of the...

common multiple of the orders in the cyclic groups, is given by the Carmichael function λ ( n ) {\displaystyle \lambda (n)} (sequence A002322 in the OEIS)...

because p is prime. Therefore, unless q divides b − 1, p divides the Carmichael function of q, which is even and equal to q − 1. Any positive multiple of...

{\displaystyle k} and above 1. Here, ϕ {\displaystyle \phi } is Euler's totient function. There are infinitely many solutions to the equation for k {\displaystyle...

and φ {\displaystyle \varphi } are respectively the Carmichael function and Euler's totient function. A root of unity modulo n is a primitive kth root of...

0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 17, ... (sequence A014197 in the OEIS) Carmichael's conjecture is that there are no 1s in this sequence. An even nontotient...

one way. 224 is the smallest k with λ(k) = 24, where λ(k) is the Carmichael function. The mathematician and philosopher Alex Bellos suggested in 2014...

Jordan's totient function, denoted as J k ( n ) {\displaystyle J_{k}(n)} , where k {\displaystyle k} is a positive integer, is a function of a positive integer...

integers below it. That is, m − φ(m) = n, where φ stands for Euler's totient function, has no solution for m. The cototient of n is defined as n − φ(n), so a...

function xy has no limit at the point (0, 0). One may consider at what points this function does have a limit. More precisely, consider the function f...

Howard John Carmichael (born 17 January 1950) is a British-born New Zealand theoretical physicist specialising in quantum optics and the theory of open...

In mathematics, a Lucas–Carmichael number is a positive composite integer n such that if p is a prime factor of n, then p + 1 is a factor of n + 1; n is...

2015 – Lucas–Carmichael number 2016 – triangular number, number of 5-cubes in a 9-cube, Erdős–Nicolas number, 211-25 2017 – Mertens function zero, sexy...