If $p$ is prime, then $F_{p-\left(\frac{p}{5}\right)}\equiv 0\bmod p$, where $F_j$ is the $j$th Fibonacci number, and $\left(\frac{p}{5}\right)$ is the Jacobi symbol.
Who first proved this? Is there a proof simple enough for an undergraduate number theory course? (We will get to quadratic reciprocity by the end of the term.)