I am thoroughly lost with how to construct this proof:
Let F(sub)n be the nth Fibonacci number.
Prove that, if 3|n then 2|F(sub)n.
Would induction be a recommendation, and if so, could anyone please recommend a base assumption to begin with?
Thank you very much for your time,
What you want to prove is that
is divisible by 2 for any positive integer n. It is easy to do that by induction on n.
If n= 1,
which is divisible by 2.
Assume that, for some k,
is divisible by 2. That is, that
for some integer m.