Hello, I asked this question earlier, but received no answer to it; I thought I had solved this problem; however, I realized that the problem

Hello,

I asked this question earlier, but received no answer to it; I thought I had solved this problem; however, I realized that the problem implicitly does not want us to use the fact that the fibonacci sequence modulo n for some n contained in N yields an infinitely recursive sequence that returns a 0 for each term indexed as a multiple of n. As a result, I am at a loss on how to approach the following problem.

Let n ∈ N.

Prove that 2 | Fn if and only if 3 | n.

Thank you for your help

All the best