Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
I tested some values of $p$; it definitely works for any $p$ above a certain bound, but $p > F(n)$ is not enough. $p > F(n+2)$ would work, but I haven't proven the actual bound yet.
Take the modulo on the left, then the modulo on the right. I omitted the bracket because it's usually assumed to be left-associative. Anyways, edited for clarity.
