A029727 Complete list of solutions to y^2 = x^3 + 17; sequence gives y values.

3, 4, 5, 9, 23, 282, 375, 378661

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

References

• L. J. Mordell, Diophantine Equations, Ac. Press, p. 246.

Crossrefs

See A029728 for further comments and references.

Programs

Magma

Sort([ Abs(p[2]) : p in IntegralPoints(EllipticCurve([0,17])) ]); // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

Mathematica

r[x_] := Reduce[y > 0 && y^2 == x^3 + 17, y, Integers]; y /. ToRules /@ Select[Table[r[x], {x, -2, 10000}], # =!= False & ] (* Jean-François Alcover, Sep 07 2011 *)

SageMath

[i[1] for i in EllipticCurve([0, 17]).integral_points()] # Seiichi Manyama, Aug 25 2019