algorithmic

#include <iostream>
#include <cmath>
#include <math.h>

using namespace std;

bool isProst(int n) {
    if(n <= 1)
        return false;
    if(n == 2)
        return true;
    for(int i = 2; i <= sqrt(n); i++)
        if(n%i == 0)
            return false;
    return true;
}

int main()
{
    int a, b;
    cin >> a >> b;
    for(int i = a; i <= b; i++)
        if(isProst(i))
            cout << i << ' ';
    return 0;
}



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#include <iostream>
#include <cmath>
#include <math.h>
#include <vector>
#include <set>

using namespace std;

int gcd (int a, int b) {
    if (b == 0)
        return a;
    else
        return gcd (b, a % b);
}
int phi (int n) {
    int result = n;
    for (int i=2; i*i<=n; ++i)
        if (n % i == 0) {
            while (n % i == 0)
                n /= i;
            result -= result / i;
        }
    if (n > 1)
        result -= result / n;
    return result;
}

int main()
{
    int n;
    cin >> n;
    cout << "Порядок Z" << n << ": " << phi(n) << '\n' << "Элементы: ";
    vector<int> vc;
    for(int i = 1; i < n; i++)
        if(gcd(i, n) == 1) {
            vc.push_back(i);
            cout << i << ' ';
        }
    cout << '\n';
    for(int i = 0; i < vc.size(); i++) {
        cout << "Элемент " << vc[i] << ": ";
        set<int> st;
        int start = vc[i];
        st.insert(start);
        for(int j = 0; j < 10000; j++) {
            start = (start * vc[i]) % n;
            st.insert(start);
        }
        cout << "("<< st.size() << "):   ";
        for (auto it = st.begin(); it != st.end(); ++it)
            cout << *it << ' ';
        cout << '\n';
    }

    return 0;
}





#include <iostream>
#include <cmath>
#include <math.h>
#include <vector>
#include <set>

using namespace std;

int main()
{
    //степени a + циклическая группа которую порождает
    int a, n;
    cin >> a >> n;
    int cur = a;
    set<int> st;
    for(int i = 1; i < 300; i++) {
        //cout << a << "^" << i << " = " << cur << "(-" << n - cur <<  ")(mod " << n << ")" << '\n';
        st.insert(cur);
        cur = (cur * a)%n;
    }

    cout << "Порождает циклическую подгруппу Z" << n << " порядка " << st.size() << ":" << '\n';

    for (auto it = st.begin(); it != st.end(); ++it)
        cout << *it << ' ';
    cout << '\n';

    cur = a;
    for(int i = 1; i < 300; i++) {
        cout << a << "^" << i << " = " << cur << "(-" << n - cur <<  ")(mod " << n << ")" << '\n';
        cur = (cur * a)%n;
    }

    return 0;
}