### Golden Powers

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

### Continued Fractions I

An article introducing continued fractions with some simple puzzles for the reader.

### Fibonacci Factors

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

# Farey Fibonacci

##### Age 16 to 18 Short Challenge Level:

Test the result for several small values of $n$ and try to decide why the absolute value appears in the formula.

What values of $n$ are you asked to prove the result for and what method of proof does this suggest?