### 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.

### And So on - and on -and On

Can you find the value of this function involving algebraic fractions for x=2000?

# Poly Fibs

##### Stage: 5 Challenge Level:

This sequence of polynomials has similarities to the sequence of Fibonnaci numbers.

Sometimes, as in this case, results are easy to state but not so easy to prove so we make an exception here in not asking for a proof of the general conjecture. It is no bad thing to cultivate a sense of what is likely to be true and a sense of curiosity about why it should be true but also to see that one needs to go on learning more to be able to do more.