# Problem 45

Solution to Problem 45. Written in Python.

Problem: 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.