### Iff

Prove that if n is a triangular number then 8n+1 is a square number. Prove, conversely, that if 8n+1 is a square number then n is a triangular number.

### Relative Powers

Weekly Problem 10 - 2007
The square of a number is 12 more than the number itself. The cube of the number is 9 times the number. What is the number?

### Nine Sum to Square

Weekly Problem 32 - 2007
One of these numbers is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?

# Generating Triples

##### Stage: 4 Challenge Level:
Here is an extract from Charlie's table:

Where is the $5^2$?
Where is the $12^2$?
Where is the $13^2$?

Where might we find a similar set of related square numbers?