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:

Use the formula for the $n$th Fibonacci number:
$F_n={1\over\sqrt5}(\alpha^n-\beta^n)$ where $\alpha$ and $\beta$
are solutions of the quadratic equation $x^2-x-1=0$ and $\alpha
> \beta.$