Question

How to find the first integer equal to the sum of its digits raised to some power in C++

Answer 1

#include <iostream>
#include <cmath>

long long digitSum(long long n) {
    long long s = 0;

    while (n > 0) {
        s += n % 10;
        n /= 10;
    }
    
    return s;
}

int main() {
    for (long long n = 2; ; n++) {
        long long s = digitSum(n);

        // Try powers k = 2..10 (enough for reasonable ranges)
        long long p = s * s;
        for (int k = 2; k <= 10; ++k) {
            if (p == n) {
                std::cout << "Found: " << n 
                          << " = (" << s << ")^" << k << "\n";
                return 0;
            }
            p *= s; // next power
        }
    }
}



/*
run:

Found: 81 = (9)^2

*/

 

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