The definition of Carmichael number is that for a composite number n, if there is a congruence formula B (n- 1) ≡ 1 (mod n) for all positive integers b that are coprime with n, then this composite number n is called Carmichael number.
On 20 16, Yu Jianchun, a logistics worker, boarded the platform of the Mathematics Department of Zhejiang University with his five major mathematical discoveries and talked with professors and doctoral students. The most valuable discovery is a set of criteria for judging Carmichael number.
Each carmichael is the product of at least three different prime numbers. Such as 561= 3 *11*17. Fermat's Theorem: Let p be a prime number, and for any integer A, there exists a(p- 1)≡ 1 (mod p). If p is a prime number and gcd(a, p)= 1, then A (p- 1) ≡ 1 (mod P) If p is a prime number and a and p are coprime, then the power of a (p- 1) is divided by.
Let P be a prime number, and A and P are coprime, then a p-a must be a multiple of P. Using Fermat's theorem, we can design a prime number determination algorithm for a given integer n, and determine the prime number of the integer n by calculating D = A (n-1) mod n. When D is not equal to1,N is definitely not a prime number. When d is equal to 1, n is probably a prime number. But there is also a complex number n that makes d = a (n- 1) ≡ 1 (mod n). For example, when a=2, the smallest complex number satisfying d= 1 is n=34 1.