OFFSET
1,1
COMMENTS
Mordell's equation has a finite number of integral solutions for all nonzero k. Gebel computes the solutions for k < 10^5. Sequence A054504 gives k for which there are no integral solutions to y^2 = x^3 + k. See A081120 for the number of integral solutions to y^2 = x^3 - n.
This is the complement of A106265. - M. F. Hasler, Oct 05 2013
Numbers k such that A081120(k) = 0. - Charles R Greathouse IV, Apr 29 2015
REFERENCES
T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, page 191.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..7757 (from Gebel, 3136 and 6789 removed by Seth A. Troisi, May 20 2019)
J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
J. Gebel, A. Petho and G. Zimmer, On Mordell's equation, Compositio Mathematica 110 (3) (1998), 335-367. MR1602064.
Eric Weisstein's World of Mathematics, Mordell Curve
MATHEMATICA
m = 99; f[_List] := (xm = 2 xm; ym = Ceiling[xm^(3/2)];
Complement[Range[m], Outer[Plus, -Range[0, ym]^2, Range[-xm, xm]^3] //Flatten //Union]); xm=10; FixedPoint[f, {}] (* Jean-François Alcover, Apr 29 2011 *)
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
T. D. Noe, Mar 06 2003
STATUS
approved