Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

//note: Erd\"os-Straus conjecture

int main(void) {
	long long N;
	cin >> N;
	if(N % 2 == 0) {
		cout << (N / 2) << ' ' << N << ' ' << N << '\n';
		return 0;
	}
	long long p;
	for(long long i = 2; i <= N; ++i) {
		if(N % i == 0) {
			p = i;
			break;
		}
	}
	long long g = N / p;
	if(p % 4 == 3) {
		long long n = (p - 3) / 4;
		cout << g * 2 * (n + 1) << ' ' << g * 2 * (n + 1) << ' ' << g * (n + 1) * (4 * n + 3) << '\n';
		return 0;
	}
	if(p % 8 == 5) {
		long long m = (p - 5) / 8;
		cout << g * 2 * (m + 1) << ' ' << g * (m + 1) * (8 * m + 5) << ' ' << g * 2 * (m + 1) * (8 * m + 5) << '\n';
		return 0;
	}
	if(p % 24 == 17) {
		long long k = (p - 17) / 24;
		cout << g * 6 * (k + 1) << ' ' << g * (k + 1) * (24 * k + 17) << ' ' << g * 6 * (k + 1) * (24 * k + 17) << '\n';
		return 0;
	}
	for(long long h = 1; h <= 3500; ++h) {
		for(long long n = h; n <= 3500; ++n) {
			for(long long w = max(n, 3 * N / 4); w <= 3500; ++w) {
				if(4 * h * n * w == N * (n * w + h * w + h * n)) {
					cout << h << ' ' << n << ' ' << w << '\n';
					return 0;
				}
			}
		}
	}
	return 0;
}