Szukanie podstawy potęgi w potędze

#include <iostream>
#include <string>
#include <cmath>
#include <vector>
#include <algorithm>
#include <conio.h>

int main()
{
    using namespace std;
    cout << "GIVE ME A NUMBER: ";
    int how_many_times;                                                     // Ile liczb ma być sprawdzonych
    cin >> how_many_times;
    cout << endl;
    vector<string>stab;
    unsigned long long *numbers = new unsigned long long[how_many_times];
    for (int i = 0; i < how_many_times; i++)                                //zapisywanie liczb do tablicy
    {
        numbers[i] = i + 1;
        unsigned long long q = 1;
        stab.push_back(to_string(numbers[i] * numbers[i]));
    }
    cout << endl;
    for (int j = 0; j < how_many_times; j++)
    {
        string buff_pow, buff_root;
        buff_pow = to_string(numbers[j] * numbers[j]);                      //Zamiana na stringi w celu sprawdzenia
        buff_root = to_string(numbers[j]);
        int li = buff_pow.length() - buff_root.length();
        int x = 0;
        while (true)
        {
            string buff_substr;
            if (buff_root.length() + x > stab[j].length())                  //Przeszukiwanie liczby za pomocą bufora
            {
                break;
            }
            if (buff_pow.length() == 1)
            {
                buff_substr = buff_pow.substr(x, x + buff_root.length());
            }
            else
                buff_substr = buff_pow.substr(x, x + buff_root.length()-1);
            if (buff_substr == buff_root)
            {
                cout << buff_root << " is a part of " << buff_pow << " (" << buff_root << " ^ 2)" << endl << endl;
                break;
            }

            x++;
        }

    }
    cout << "---------------------------------------------------------------------END";
    delete[] numbers;
    stab.clear();
    _getch();
    return 0;
}