http://www.openproblemgarden.org/op/fibonacci_divisibility Comments for "Wall-Sun-Sun primes and Fibonacci divisibility" en http://www.openproblemgarden.org/op/fibonacci_divisibility <table cellspacing="10"> <tr> <td> Author(s): <a href="/kpz_equation_central_limit_theorem"></a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/number_theory_0">Number Theory</a> » <a href="/category/computational_number_theory">Computational N.T.</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; For any prime <img class="teximage" src="/files/tex/928cd9d544fdea62f88a627aaee28c416c4366c0.png" alt="$ p $" />, there exists a Fibonacci number divisible by <img class="teximage" src="/files/tex/928cd9d544fdea62f88a627aaee28c416c4366c0.png" alt="$ p $" /> exactly once. </div> <p>Equivalently:</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; For any prime <img class="teximage" src="/files/tex/a9737aaa01b2918b7e8ab9f12ab0a7c463381427.png" alt="$ p&gt;5 $" />, <img class="teximage" src="/files/tex/8f6ab14c3cc11c005c9b97778062620c197ff66d.png" alt="$ p^2 $" /> does not divide <img class="teximage" src="/files/tex/e1a04059df8fc3e49db781f306092d0d564732e3.png" alt="$ F_{p-\left(\frac p5\right)} $" /> where <img class="teximage" src="/files/tex/d8d0b3deced8bb07e56b3da3337f2d8c7db060a1.png" alt="$ \left(\frac mn\right) $" /> is the Legendre symbol. </div> </tr></td> </table> </td> </tr> </table> Fibonacci prime Number Theory Computational Number Theory http://www.openproblemgarden.org/op/fibonacci_divisibility#comment Sat, 14 Jun 2008 02:27:17 +0200 adudzik 822 at http://www.openproblemgarden.org