### Golden Powers

You add 1 to the golden ratio to get its square. How do you find higher powers?

### 2^n -n Numbers

Yatir from Israel wrote this article on numbers that can be written as $2^n-n$ where n is a positive integer.

### Poly Fibs

A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.

# Production Equation

##### Stage: 5 Challenge Level:
The general method of solving problems where there is a formula for the transition from one phase to the next is to solve either a difference equation (such as this), or a differential equation, according to whether the model is discrete or continuous.