Multiply two positive integers using recursion

#include <iostream>
#include <string>
#include <limits>
using namespace std;

// This function uses recursion to
// multiply two positive integers, or zero.
int mult(int i, int n)
{
    if (n == 0) return 0; // Base case.
    else if (n == 1) return i; // Base case.
    else
    {
        // Recurrence relation.
        return i + mult(i, n - 1);
    }
}

int main()
{
    string int_1_string; // Input number to multiply.
    string int_2_string; // Input number of times.
    int int_1 = 0; // Number to multiply converted to int.
    int int_2 = 0; // Number of times converted to int.
    int product = 0; // Result of multiplication.

    cout << "This program shows how recursion can be\n"
        "used to multiply two positive integers.\n"
        "What integer would you like to multiply? ";
    getline(cin, int_1_string); // Get number to multiply.
    int_1 = stoi(int_1_string); // Convert to int.
    while (int_1 < 0) // If it's not positive or zero,
    {
        cout << "Please enter an integer greater than or"
            " equal to zero. ";
        getline(cin, int_1_string); // Get new input.
        int_1 = stoi(int_1_string); // Convert it to int.
    }

    cout << "How many times would you like to multiply it? ";
    getline(cin, int_2_string); // Get number of times.
    int_2 = stoi(int_2_string);  // Convert to int.
    while (int_2 < 0) // If it's not positive or zero,
    {
        cout << "Please enter an integer greater than or"
            " equal to zero. ";
        getline(cin, int_2_string); // Get new input.
        int_2 = stoi(int_2_string); // Convert it to int.
    }

    product = mult(int_1, int_2); // Calculate the result.

    // Display the result.
    cout << "The product of " << int_1 << " and "
        << int_2 << " is " << product << ".\n";

    // End the program.
    return 0;
}