I have to solve the following problem and I have a few questions: Consider the Fibonacci sequence defined as $F_n:=2F_{n-1}+F_{n-2}$ with $F_0=1$ and $F_1=1$. Now, I need to prove that for any odd prime p $$F_p=(5/p) \mod p $$. My first question is, why is the fibonacci sequence defined with a $2$ multiplying $F_{n-1}$, and I don't really know how to prove this. I tried using Gauss´s Quadratic Reciprocity, but I can´t reach the conclusion I want.
2026-04-15 13:54:25.1776261265
Divisibility of Fibonacci Sequence mod prime
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