id: 02360641
dt: j
an: 2004d.03404
au: Bloms, Michelle; Brown, Lesley; Ellis, Larry; Farmer, Terence; Goward,
Russell; Graham, Meridith Tara; Hulsen, David; Martin, Jeremy;
McKinnie, Kelly; Neuerburg, Kent; Schoen, Keary; Terwilleger, Erin;
Thompson, Nikki Janelle
ti: Integer points on cubic twists of elliptic curves.
so: Pi Mu Epsilon J. 11, No. 10, 515-518 (2004).
py: 2004
pu: Worcester Polytechnic Institute (WPI), Mathematical Sciences, Worcester, MA
la: EN
cc: F60
ut:
ci:
li:
ab: The problem of finding out whether a given integer $D$ may be written as
the sum of two rational cubes $x^3+y^3=D$ is one of the oldest problems
in number theory. In this paper, we conduct an experimental
investigation into the frequency of $D$ which admit two distinct
relatively prime solutions. We also evaluate this data against a
hypothesis which does afford an explanation for why $D$ which admit
three relatively prime solutions are quite rare, and why no $D$ has
been found which may be expressed in four different ways as a sum of
relatively prime cubes. (From the introduction)
rv: