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 (...

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

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

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...

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...

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

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...

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

}}(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...

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

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...

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...

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)...

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...

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

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)...

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...

\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...

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...

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...

known as Quantum Trajectory Theory developed by Carmichael. Other contemporaneous works on wave-function-based Monte Carlo approaches to open quantum systems...

Kumho Tire Co. v. Carmichael, 526 U.S. 137 (1999), is a United States Supreme Court case that applied the Daubert standard to expert testimony from non-scientists...

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...

{\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...

\varphi (m)>\varphi (n)} where φ {\displaystyle \varphi } is Euler's totient function. The first few sparsely totient numbers are: 2, 6, 12, 18, 30, 42, 60,...

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...

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