Carmichael number - Wikipedia
Carmichael numbers are composite numbers which have the same property. Carmichael numbers are also called Fermat pseudoprimes or absolute Fermat pseudoprimes. A Carmichael number will pass a Fermat primality test to every base relatively prime to …
Carmichael Number -- from Wolfram MathWorld
A Carmichael number is an odd composite number n which satisfies Fermat's little theorem a^(n-1)-1=0 (mod n) (1) for every choice of a satisfying (a,n)=1 (i.e., a and n are relatively prime) with 1<a<n.
Carmichael Numbers - GeeksforGeeks
2023年5月8日 · A number n is said to be a Carmichael number if it satisfies the following modular arithmetic condition: power(b, n-1) MOD n = 1, for all b ranging from 1 to n such that b and n are relatively prime, i.e, gcd(b, n) = 1 . Given a positive integer n, find if it is a Carmichael number.
Carmichael numbers - OeisWiki - The On-Line Encyclopedia of ...
2020年1月3日 · Carmichael numbers are important because they pass the Fermat primality test but are not actually prime. Since Carmichael numbers exist, this primality test cannot be relied upon to prove the primality of a number, although it can still …
There are in nitely many Carmichael numbers, which is a hard theorem [1]. It is possible to verify an integer n is a Carmichael number without using the de nition, which means you don’t have to check a n 1 1 mod n for all a such that (a;n) = 1.
Number Theory - Carmichael Numbers - Stanford University
Recall Carmichael numbers are composite numbers that almost always fool the Fermat primality test. We can show that Carmichael numbers must have certain properties.
It is possible to verify that an integer n is a Carmichael number without using the de nition, so not having to check a n 1 1 mod n for all a that are relatively prime to n. Instead we can check a property of the prime factorization of n known as Korselt’s criterion.