Determine which Fibonacci numbers are even (a) Determine which Fibonacci numbers are even. Use a form of mathematical induction to prove your conjecture.
(b) Determine which Fibonacci numbers are divisible by 3. Use a form of mathematical induction to prove your conjecture

I understand that for part a that all multiples of 3 of n are even. So F(0),F(3),F(6)... I just don't understand how to prove it.

For part B it is the same thing except multiples of 4

Please help, thank you!
Hint: You can look at the first few terms of the sequence modulo $n$, and then conclude a pattern (because each term is based upon the previous two). The first few terms of the Fibonacci sequence modulo $2$ are

$1,1,0,1,1,0,1,1,0,1,1,0,\ldots$

The first few terms of the Fibonacci sequence modulo $3$ are

$1,1,2,0,2,2,1,0,1,1,2,0,\ldots$

Now how can you formalize this argument using induction? 

Another hint: you may want multiple base cases.
1,1,2,3,5,8 . . .
an even number and an odd number added together is odd, an odd number plus and odd number is even.