### 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?

# Plus or Minus

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

The Golden Ratio is one of the roots of the equation $x^2-x-1=0$ and the $n$th Fibonacci number is$F_n={1\over\sqrt5}(\alpha^n-\beta^n)$ where $\alpha$ and $\beta$ are solutions of the quadratic equation $x^2-x-1=0$ and $\alpha > \beta$ hence the many connections between Fibonacci numbers and the Golden Ratio.