## What is the Triangular number?

A number which can be represented by a triangular array of dots. 1, 3, 6, 10, are all triangular numbers.

The nth triangular number is n(n+1)/2.

All integer is the sum of at most 3 triangular numbers.

If t is a triangular number, 8t+1 is a square.

The square of the nth triangular number is equal to the sum of the first n cubes.

Certain triangular numbers are also squares, but no triangular number can be a third, fourth or fifth power.