A029727 - OEIS

A029727

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

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

LINKS

Table of n, a(n) for n=1..8.

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 *)

PROG

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

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

CROSSREFS

See A029728 for further comments and references.

Sequence in context: A257041 A346603 A056797 * A086186 A365578 A014463

Adjacent sequences: A029724 A029725 A029726 * A029728 A029729 A029730

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane

STATUS

approved