1,1

Mordell's equation has a finite number of integral solutions for all nonzero n. Gebel computes the solutions for n < 10^5. Sequence A081121 gives n for which there are no integral solutions to y^2 = x^3 - n. See A081119 for the number of integral solutions to y^2 = x^3 + n. - T. D. Noe, Mar 06 2003

Numbers n such that A081119(n) = 0. - Charles R Greathouse IV, Apr 29 2015

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, page 192.

J. Gebel, A. Petho and H. G. Zimmer, On Mordell's equation, Compositio Mathematica 110 (3) (1998), 335-367.

T. D. Noe, Table of n, a(n) for n = 1..6603 (from Gebel)

Pantelis Andreou, Stavros Konstantinidis, and Taylor J. Smith, Improved Randomized Approximation of Hard Universality and Emptiness Problems, arXiv:2403.08707 [cs.DS], 2024. See p. 16.

Ryan D'Mello, Marshall Hall's Conjecture and Gaps Between Integer Points on Mordell Elliptic Curves, arXiv preprint arXiv:1410.0078, 2014

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]

Eric Weisstein's World of Mathematics, Mordell Curve

m = 155; 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 28 2011 *)

Cf. A081119, A081121.

Sequence in context: A164018 A156793 A081715 * A190612 A270431 A315832

Adjacent sequences: A054501 A054502 A054503 * A054505 A054506 A054507

nonn,nice

N. J. A. Sloane, Apr 08 2000

Apostol gives all values of n < 100. Extended by David W. Wilson, Sep 25 2000

approved