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A029727 Complete list of solutions to y^2 = x^3 + 17; sequence gives y values. 10

%I #17 Sep 08 2022 08:44:50

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

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

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

%t 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 *)

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

%o (SageMath) [i[1] for i in EllipticCurve([0, 17]).integral_points()] # _Seiichi Manyama_, Aug 25 2019

%Y See A029728 for further comments and references.

%K nonn,fini,full

%O 1,1

%A _N. J. A. Sloane_

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)