Cod sursa(job #2451660)

Utilizator PatrickCplusplusPatrick Kristian Ondreovici PatrickCplusplus Data 27 august 2019 16:18:12
Problema Invers modular Scor 10
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 1.05 kb
// A * x congruent cu 1 modulo N x = invers modular
// Pentru a exista inversul modular cmmdc(A, N) = 1
// Teorema lui Euler: A^(phi(N)) congruent cu 1 modulo N => A * A^(phi(N) - 1) congruent cu 1 modulo N => A^(phi(N) - 1) este inversul modular a lui A
#include <bits/stdc++.h>

using namespace std;

ifstream fin("inversmodular.in");
ofstream fout("inversmodular.out");

long long A, N;

int phi(int x)
{
    int result = x;
    for (int i = 2; i * i <= x; ++i)
    {
        if (x % i == 0)
        {
            while (x % i == 0)
                x = x / i;
            result *= (i - 1);
            result /= i;
        }
    }
    if (x > 1)
    {
        result *= (x - 1);
        result /= x;
    }
    return result;
}

long long log2pow(long long n, long long p)
{
    if (p == 0)
        return 1;
    long long x = log2pow(n, p / 2);
    if (p % 2 == 0)
        return ((x % N) * (x % N)) % N;
    return n * x % N * x % N;
}

int main()
{
    fin >> A >> N;
    fout << log2pow(A, phi(N) - 1);
    return 0;
}