In number theory, Carmichael's theorem, named after the American mathematician R. D. Carmichael, states that, for any nondegenerate Lucas sequence of...

and the value of Carmichael's function, λ(5), must be a divisor of 4. The divisor 1 does not satisfy the definition of Carmichael's function since a 1...

{\displaystyle n} must be coprime. The theorem is further generalized by some of Carmichael's theorems. The theorem may be used to easily reduce large powers...

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. The...

{\displaystyle {\mathcal {Z}}(W_{n})} . Carmichael's theorem Wilson prime Kaprekar's constant Fermat's little theorem Babczynski theorem Palindromic numbers Harshad...

Fermat's Little Theorem although they are not primes), Carmichael's totient function conjecture, Carmichael's theorem, and the Carmichael function, all...

primitive. Carmichael's theorem states that all but finitely many of the terms in a Lucas sequence have a primitive prime factor. Indeed, Carmichael (1913)...

important theorems relating to modular arithmetic: Carmichael's theorem Chinese remainder theorem Euler's theorem Fermat's little theorem (a special...

Brun's theorem (number theory) Brun–Titchmarsh theorem (number theory) Carmichael's theorem (Fibonacci numbers) Chebotarev's density theorem (number...

Fermat's Little Theorem does not hold. This fact precludes the use of that theorem as an absolute test of primality. The Carmichael numbers form the...

prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). As a result, 8 and 144 (F6 and F12) are the only Fibonacci numbers...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...

2307/2031878, JSTOR 2031878 Yabuta, M. (2001), "A simple proof of Carmichael's theorem on primitive divisors" (PDF), Fibonacci Quarterly, 39 (5): 439–443...

Fk, but "at least" one new characteristic prime from Carmichael's theorem. Carmichael's Theorem applies to all Fibonacci numbers except four special cases:...

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...

proving Carmichael's conjecture. However if it exists then infinitely many counterexamples exist as asserted by Ford. Another way of stating Carmichael's conjecture...

infinitely often. However, no number m is known with multiplicity k = 1. Carmichael's totient function conjecture is the statement that there is no such m...

follows from Euler's theorem. More generally, for any e and d satisfying ed ≡ 1 (mod λ(n)), the same conclusion follows from Carmichael's generalization of...

than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself...

Theorem is a theorem in number theory, originally stated by Pierre de Fermat in 1637 and proven by Andrew Wiles in 1995. The statement of the theorem...

postulate is also called the Bertrand–Chebyshev theorem or Chebyshev's theorem. Chebyshev's theorem can also be stated as a relationship with π ( x )...

The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and...

In mathematics, the Hardy–Ramanujan theorem, proved by Ramanujan and checked by Hardy states that the normal order of the number ω ( n ) {\displaystyle...

important class of pseudoprimes that come from Fermat's little theorem. Fermat's little theorem states that if p {\displaystyle p} is prime and a {\displaystyle...

for the second equivalence to hold, since if p is prime, Fermat's little theorem states that a p − 1 ≡ 1 ( mod p ) {\displaystyle a^{p-1}\equiv 1{\pmod...

sequence of "Fermat near misses" defined, in reference to Fermat's Last Theorem, as numbers of the form 1 + z 3 {\displaystyle 1+z^{3}} , which are also...

function such as a step function. Carmichael's totient function conjecture was stated as a theorem by Robert Daniel Carmichael in 1907, but in 1922 he pointed...

2024-05-30. Cohen, Henri (2007). "Consequences of the Hasse–Minkowski Theorem". Number Theory Volume I: Tools and Diophantine Equations. Graduate Texts...

_{k=1}^{n}k\right)^{2}.} This identity is sometimes called Nicomachus's theorem, after Nicomachus of Gerasa (c. 60 – c. 120 CE). Nicomachus, at the end...

same for the three elements). The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula...