The Fibonacci numbers are defined by , and

Prove if , then

This is one of those times where it's easy to see intuitively, it's hard to see formally.

Considering the Fibonacci sequence

It falls into a pattern of

From, as the first term is even, it's clear to see that every third term beginning from is divisible by 3, as it is the sum of the 2 previous numbers which are odd.

But this just scaffolding, scrap work.

Any tips on how to codify this formally?