Question

From Project Euler, 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 T_(285) = P_(165) = H_(143) = 40755.

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

Here’s the question.
It’s pretty simple and straightforward, but the thing is, my program runs into a glitch, the moment the value of the triangle number exceeds the maximum value that you can have in int data type. I’ve tried searching for the net for other data types but no success.

Code

     #include<stdio.h>
     int main(void)
     {
        int i,j,t,h,p,k;
        int n=10000;
        for(i=0;i<n;i++)
        {
            t=(i*(i+1))/2;
            for(j=0;j<n;j++)
            {   
                h=j*(2*j-1);
                if(h>t)
                break;
                if(h==t)
                {   
                    //printf("%d %d\n",h,t);
                    for(k=0;k<n;k++)
                    {
                        p=(k*(3*k-1))/2;
                        if(p>h)
                        break;
                        if(p==h)
                        {
                            printf("%d %d\n",p,i);
                            break;
                        }   
                    }   
                }

            }   
        }       
        printf("done\n");
        return(0);
     }

Answer 1

Try unsigned long long. It should work.