Congruent Equation (inversion yuan, linear congruence equation minimal solution

# The meaning of problems

Given a, b, x is obtained about the minimum equation ax ≡ 1 (mod b) of

Input to ensure a certain solvability

2 ≤ a,b ≤ 2*10⁹

# Explanations

ax ≡ 1 (mod b)

ax+by=1

REPRESENTATION OF GENERAL SOLUTION:

x = x₀ + b * k

y = y ₀ - a * k

Therefore, x ₀  % B x can take is the minimum

Finally, take the remainder being used skills: the number of re-mold after mold plus die once

 1 #include<bits/stdc++.h>
 2 #define ll long long
 3 using namespace std;
 4 ll a,b;
 5 ll exgcd(ll a,ll b,ll &x,ll &y){
 6     if(b==0){
 7         x=1;y=0;
 8         return a;
 9     }
10     ll d =exgcd(b,a%b,y,x);
11     y-=a/b*x;
12 }
13 int main(){
14     cin>>a>>b;
15     ll x,y;
16     exgcd(a,b,x,y);
17     cout<<(x%b+b)%b<<endl;
18 }