Multiplication inverse element

If X exists in numbers A and C and A * x = 1 (mod C), X is called the multiplication inverse element of A to C.
What is the role of reverse element? Let's take a look at the following example:
12/4 mod 7 =? Obviously, the result is 3.
For the number pair (), we can know that X = 2 is the multiplication inverse element of 4 to 7, that is, 2*4 = 1 (mod 7)
So we have (12/4) * (4*2) = (?) * (1) (mod 7)
Division is perfectly converted to multiplication
Theoretical Basis:
F/A mod c =?
If a * x = 1 (mod c) exists)
Then, if the two sides are multiplied at the same time, f * x =? (Mod C)
Conditions for Establishment
(1) modulus equation A * x = 1 (mod C)
(2) A | f (F % A = 0)
Baidu Encyclopedia:
If AX = 1 Mod f, A is called the multiplication inverse element of Mod f as X. It can also be expressed as ax limit 1 (mod F ).
When A and F are mutually Prime, A has a unique solution to the multiplication inverse element of the modulo F. If there is no mutual element, there is no solution. If F is a prime number, any number from 1 to F-1 is mutually prime with F, that is, there is a multiplication inverse element about the modulo F between 1 and F-1.
For example, to obtain the multiplication inverse element of the modulo 14:
14 = 5*2 + 4
5 = 4 + 1
Description: there are 5 inverse elements of multiplication of 14 in the form of 5 and 14.
1 = 5-4 = 5-(14-5*2) = 5*3-14
Therefore, the multiplication inverse element of the 5 modulo 14 is 3.