### 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?

### Summing Squares

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?