TITLE: Calculating Fibonacci numbers
QUESTION [5 upvotes]: In my book they calculated the $28$th Fibonacci number and said $F_{28} = 3 \times 13 \times 19 \times 281 = 317811$. This made me wonder if there was an easier way to find the $28$th Fibonacci number than by doing it by hand.

REPLY [2 votes]: Unfortunately this requires (sometimes) a calculator to compute. You could potentially use the following:
Let $\phi = \frac{1+\sqrt5}{2}$
$F_{n}=\frac{\phi^x-(1-\phi)^x}{\sqrt5}$