… you can find the following ‘finite sums’…
Since , it follows from (2) that devides …
Prove that if Fn is the "nth" Fibonacci number that if 3|n (3 divides n) then 2|Fn
(2 divides the nth Fibonacci number).
THIS PROBLEM HAS BEEN SOLVED.
THANKS TO ALL WHO HELPED!!
Read this post here, it is even more general than what you need. (It uses the Euclidean Algorithm)
Proofs for the formulas that appear above in this thread:
In fact this gets even more general since we have: (this may be proven by induction quite easily since
And it follows that we have:
From there check that is a multiple of