## Triangular, pentagonal, and hexagonal

### Problem 45

Published on Friday, 6th June 2003, 06:00 pm; Solved by 43723; Difficulty rating: 5%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.