Problem 45 Triangular, pentagonal, and hexagonal （暴力）

Triangular, pentagonal, and hexagonal

Problem 45

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

Triangle
T_n=n(n+1)/2
1, 3, 6, 10, 15, ...Pentagonal
P_n=n(3n−1)/2
1, 5, 12, 22, 35, ...Hexagonal
H_n=n(2n−1)
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.

Answer:

1533776805Completed on Sun, 30 Oct 2016, 12:17

代码：

#include <iostream>#include <cmath>using namespace std; int main(){    int n = 143;    while (1)    {    n++;    //Hexagonal        double h = n * (2 * n - 1);         double Triangle = (sqrt(1 + 8 * h) - 1) / 2;        double Pentagonal = (sqrt(1 + 24 * h) + 1) / 6;        double T = (int)Triangle;        double P = (int)Pentagonal;         if (T == Triangle && P == Pentagonal)        {            long long ans = n * (2 * n - 1);              cout<<ans<<endl;            break;        }     }    return 0;}