Project Euler task 45

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

Triangle		Tn=n(n+1)/2		1, 3, 6, 10, 15, ...
Pentagonal		Pn=n(3n1)/2		1, 5, 12, 22, 35, ...
Hexagonal		Hn=n(2n1)		1, 6, 15, 28, 45, ...

It can be verified that T₂₈₅ = P₁₆₅ = H₁₄₃ = 40755.

Find the next triangle number that is also pentagonal and hexagonal.

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#include < iostream >

#include < math.h >

using namespace std;

int main() {

long int x = 0;

for (int y = 1; y < 1000000; y++) {

long double fx = sqrt((long double) 3 * y * y - 2);

if (fx - floor(fx) > 0)

continue;

x = floor(fx);

long double fn = (fx + 1) / 6;

if (fn - floor(fn) > 0)

continue;

long double fm = ((double) y + 1) / 4;

if (fm - floor(fm) > 0)

continue;

long long int n = (x + 1) / 6; // pentagonal

cout << n * (3 * n - 1) / 2 << " : " << x << " " << y << endl;

}

return 0;

}