Inverse meta-summary

Inverse element:

Define to A∈ZM, exist B∈zm, make a+b≡0 (mod m), then B is an additive inverse of a, kee b=-A. Defined on A∈ZM, the presence of B∈ZM, which makes axb≡1 (mod m), is said to be a multiplication inverse of B.

(b/a) (mod n) = (b * x) (mod n). x represents the inverse of a. and a*x≡1 (mod n) Note: The inverse is only present when A and n coprime

To find a minimum positive integer x (inverse), so that a times X to N of the remainder equals 1 of the remainder of N,

Fermat theorem:

　　If a is an integer, p is a prime number, and A,p coprime (that is, there is only one convention of 1), then the remainder of a (p-1) divided by P is constant equal to 1.

Can be recorded as:

The inverse can be obtained (when M is a prime number)

Extended Euclid:

When GCD (A, m), any set of integer solutions of Ab+mx=1 (b,x), B is the multiplicative inverse of a

under normal circumstances (GCD (A, m)! = 0):

(A/b) mod m = a mod (MB)/b;

Inverse meta-summary