Fibonacci

Wall-Sun-Sun primes and Fibonacci divisibility ★★

Author(s):

Conjecture For any prime $p$ , there exists a Fibonacci number divisible by $p$ exactly once.

Equivalently:

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.

Posted by adudzik
updated June 14th, 2008