Problem 45

Triangular, pentagonal, and hexagonal

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(3n1)/2 |
1, 5, 12, 22, 35, ... | ||

Hexagonal | H_{n}=n(2n1) |
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.

**
These problems are part of
Project Euler
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CC BY-NC-SA 2.0 UK
**