public static long Problem45()
{
/*
* 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(3n−1)/2 1, 5, 12, 22, 35, ...
* Hexagonal Hn=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.
*/
long n = 286L;
long l = 0L;
do
{
l = (n * (n + 1)) / 2;
n = n + 1;
} while (!Formulas.isTriangular(l) || !Formulas.isPentagonal(l) || !Formulas.isHexagonal(l));
return(l);
}
public static long Problem44()
{
int result = 0;
bool notFound = true;
int i = 1;
while (notFound)
{
i++;
int n = i * (3 * i - 1) / 2;
for (int j = i - 1; j > 0; j--)
{
int m = j * (3 * j - 1) / 2;
if (Formulas.isPentagonal(n - m) && Formulas.isPentagonal(n + m))
{
result = n - m;
notFound = false;
break;
}
}
}
return(result);
}