http://openproblemgarden.org/op/quartic_rationally_derived_polynomials Comments for "Quartic rationally derived polynomials" en http://openproblemgarden.org/op/quartic_rationally_derived_polynomials#comment-6913 <p>Hyperlink in the bibliography is no longer valid, but the article can be found at: http://web.archive.org/web/20011127182208/http://www.geocities.com/teufel_pi/papers/rdp.pdf</p> Wed, 16 Feb 2011 10:02:59 +0100 Comet comment 6913 at http://openproblemgarden.org http://openproblemgarden.org/op/quartic_rationally_derived_polynomials <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/buchholz_ralph_h">Buchholz</a>; <a href="/category/macdougall_james_a">MacDougall</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/number_theory_0">Number Theory</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>Call a polynomial <img class="teximage" src="/files/tex/a72fcb0a006c3c2afb3ba69722ccdb2599b83e90.png" alt="$ p \in {\mathbb Q}[x] $" /> <em>rationally derived</em> if all roots of <img class="teximage" src="/files/tex/928cd9d544fdea62f88a627aaee28c416c4366c0.png" alt="$ p $" /> and the nonzero derivatives of <img class="teximage" src="/files/tex/928cd9d544fdea62f88a627aaee28c416c4366c0.png" alt="$ p $" /> are rational.</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; There does not exist a quartic rationally derived polynomial <img class="teximage" src="/files/tex/a72fcb0a006c3c2afb3ba69722ccdb2599b83e90.png" alt="$ p \in {\mathbb Q}[x] $" /> with four distinct roots. </div> </tr></td> </table> </td> </tr> </table> Buchholz, Ralph H. MacDougall, James A. derivative diophantine elliptic polynomial Number Theory http://openproblemgarden.org/op/quartic_rationally_derived_polynomials#comment Sat, 17 May 2008 05:53:07 +0200 mdevos 791 at http://openproblemgarden.org