045.cpp

#include <iostream>
using namespace std;

bool is_tri(unsigned  x)
{
        //solve n by iteration
        float n=1;
        float n1=1;
        do {
                n=n1;
                n1 = x/(n+1)+n/2;
        } while (n!=n1);
        return (n == (int)n); //is integer
}

bool is_pent(unsigned x)
{
        //solve n by iteration
        double n=1;
        double n1=1;
        do {
                n=n1;
                n1 = n-(n*(3*n-1)-2*x)/(6*n-1);//newton's method
        } while (n!=n1);
        return (n == (int)n); //is integer
}

int main()
{
        //for each hexagonal no, test if it is also a triangle no and pentagonal number
        for (long n=144;n>0;n++) {
                unsigned  no = n*(2*n-1);
                if (is_tri(no) && is_pent(no)) {
                        cout << no << endl;
                        break;
                }
        }
        return 0;
}