Abstract
has a rational solution. An extensive compilation of the older history of the problem is given in Dickson [6]. Within the past century, researchers have tried to exploit (either explicitly or unknowingly) the fact that the curve (0.1) is in fact an elliptic curve. During the nineteenth century, Lucas, and later Sylvester, used a descent argument to prove that (0.1) had no solution for infinitely many D in certain congruence classes mod 9 and 18 (see [6], Ch. XXI). Zagier and Kramarz [19] have produced a great deal of numerical evidence about the L-series of the curves; based on these computations, they have argued heuristically that for
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
