Multiply inverse (go)

definition : The K value satisfying a*k≡1 (mod p) is a multiplicative inverse of p. 　
Why do we have to multiply the inverse element? 　
when we ask for (A/b) mod P's value, and a is large, and cannot directly obtain a A/b value, we will use the multiplication inverse.
We can use the B to multiply the inverse k of p, multiply a by the K-mode p, ie (a*k) mod p. The result is equivalent to (A/b) mod p.

Certificate:　
according to B*k≡1 (mod p) there is b*k=p*x+1.
k= (p*x+1)/b.
put K into (a*k) mod p, get: (A * (p*x+1)/b) mod p
= ((a*p*x)/b+a/b) mod p
=[((a*p*x)/b) mod p + (A/b)] mod p
=[(p* (a*x)/b) mod p + (A/b)] mod p
//p*[(a*x)/b] MoD p=0
so the original equals: (A/b) mod p

Multiply inverse (go)