我的 C++ 程序的行为很奇怪，错误的 output？

Question

I want to view all solution for: X^12≡1(mod27) So I wrote the following C++ program which outputs only 1 even though 8 and 10 are possible values for x too.

Why is that?

#include <iostream>
#include <cmath>

int main() {
    for (int i = 0; i <= 2700000; ++i) {
        if (int(pow(i, 12))% 27 == 1) {
            std::cout << i << std::endl;
        }
    }
    std::cout << "Hello, World!" << std::endl;
    return 0;
}

Answer 1

The inbuild pow() function is not capable of handling so large number. Rather we have to use custom function to achieve that.

Here it is

#include <iostream>
#include <cmath>

long long binpow(long long a, long long b, long long m) {
    a %= m;
    long long res = 1;
    while (b > 0) {
        if (b & 1)
            res = res * a % m;
        a = a * a % m;
        b >>= 1;
    }
    return res;
}

int main() {
    for (int i = 0; i <= 2700000; ++i) {
        if (binpow(i, 12, 27) == 1) {
            std::cout << i << std::endl;
        }
    }
    std::cout << "Hello, World!" << std::endl;
    return 0;
}

You can read more about that function from here: https://cp-algorithms.com/algebra/binary-exp.html

Answer 2

Oh, that's because you're using int s to calculate 12th powers, which are very large numbers. Int can only store numbers up to 2147483647, so use long long ints instead which can be much larger.

I rewrote your code and got this output: 1 8 10 17 19 26 28

#include <iostream>
#include <cmath>

int main()
{
    for (int i = 0; i <= 2700000; ++i)
    {
        long long int power = pow(i, 12);
        int mod = power % 27;
        if (mod == 1)
            std::cout << i << std::endl;
    }

    std::cin.get();
    return 0;
}