Extended gcd inversion yuan

When the modulus is a prime number can inverse yuan by Fermat's little theorem.

When modulus is a composite number, Fermat's little theorem fails in most cases, this time, only the modulus co-prime numbers have an inverse element (composite number satisfy Fermat's little theorem called pseudo prime numbers, we need to discuss this issue open a new blog up).

(For a number n, and with it all of its mass is less than the number of the multiplicative group modulo n form a cross)

gcd is the greatest common divisor gcd is extended in a logarithmic x, Y after the gcd, a set of solutions is given a, b, such that

a*x+b*y=gcd(x,y)

Easy to see, if y is the modulus, and gcd x and y is 1,

a*x+b*y=1

a * x% y = 1

According to the definition of the inverse, when a mold is inverse element of x y.

int exgcd(int a,int b,int &x,int &y){
    if(b==0){
        x=1;
        y=0;
        return a;
    }
    int g=exgcd(b,a%b,x,y);
    int t=x;
    x=y;
    y=t-(a/b)*y;
    return g;
}