A134105 Complete list of solutions to y^2 = x^3 + 297; sequence gives x values.

-6, -2, 3, 4, 12, 34, 48, 1362, 93844

Offset: 1

Author

Klaus Brockhaus, Oct 08 2007

Keywords

• sign
• fini
• full

Comments

For corresponding y values and examples see A134104.

The parameter -297 of the curve corresponds to A200218(1). a(9)=A200216(1). - Artur Jasinski, Nov 29 2011

Crossrefs

Cf. A134104, A134103, A134107, A029728, A134042, A134074.

Programs

Magma

Sort([ p[1] : p in IntegralPoints(EllipticCurve([0, 297])) ]); /* adapted from A029728 */

Mathematica

sol[x_] := Solve[y > 0 && x^3 - y^2 == -297, y, Integers];
Reap[For[x = 1, x < 10^5, x++, sx = sol[x]; If[sx != {}, xy = {x, y} /. sx[[1]]; Print[xy]; Sow[xy]]; sx = sol[-x]; If[sx != {}, xy = {-x, y} /. sx[[1]]; Print[xy]; Sow[xy]]]][[2, 1]][[All, 1]] // Sort (* Jean-François Alcover, Feb 07 2020 *)

SageMath

[i[0] for i in EllipticCurve([0, 297]).integral_points()] # Seiichi Manyama, Aug 26 2019