# Fibonacci

## Wall-Sun-Sun primes and Fibonacci divisibility ★★

Author(s):

\begin{conjecture} For any prime $p$, there exists a Fibonacci number divisible by $p$ exactly once. \end{conjecture}

Equivalently:

\begin{conjecture} For any prime $p>5$, $p^2$ does not divide $F_{p-\left(\frac p5\right)}$ where $\left(\frac mn\right)$ is the Legendre symbol. \end{conjecture}

Keywords: Fibonacci; prime