The Fibonnaci sequence where each term is the sum of the preceding two terms, that is $f_{n+2}=f_{n+1}+f_n$, has the first two terms $f_0=0$ and $f_1=1$.

For which values of $n$ is the Fibonnaci number $f_n$ even?

Which Fibonnaci numbers are divisible by 3?

Prove general results for the occurrence of even Fibonnaci numbers in the sequence and for the occurrence of multiples of 3.