Fibonacci sequences in $\mathbb F_p$

TL;DR

This paper proves a conjecture about Fibonacci sequences in finite fields using elementary algebra, providing a simple proof that extends to other recursive sequences.

Contribution

It offers a straightforward, elementary proof of Gica's conjecture and generalizes the result to other recursive sequences.

Findings

Proves Gica's conjecture on Fibonacci sequences in finite fields

Provides a simple, elementary proof method

Extends the proof technique to other recursive sequences

Abstract

We prove a conjecture due to Gica (Fibonacci Quarterly, 2008). Our proof is simple, uses only elementary abstract algebra, and generalizes to other recursive sequences.