A133475 Integers n such that n^3 + n^2 - 9*n + 16 is a square.

-4, -3, -1, 0, 1, 3, 5, 11, 15, 28, 47, 55, 81, 549, 1799, 8361

Offset: 1

Author

Mohamed Bouhamida, Nov 29 2007

Keywords

• sign
• full
• fini

Comments

The set of x values of integral points on the elliptic curve y^2 = x^3 + x^2 - 9*x + 16.

Examples

			0^3 + (-5)^2 + (-9) = 4^2, 1^3 + (-4)^2 + (-8) = 3^2, 3^3 + (-2)^2 + (-6) = 5^2
		

Crossrefs

Cf. A117950, A132411, A132414, A002522, A028872.

Programs

Magma

P := PolynomialRing(Integers()); {x: x in Sort([ p[1] : p in IntegralPoints(EllipticCurve(n^3 + n^2 - 9*n + 16)) ])};

Mathematica

ok[x_] := Reduce[{y^2 == x^3 + x^2 - 9*x + 16, y >= 0}, y, Integers] =!= False; Select[Table[x, {x, -4, 10000}], ok ] (* Jean-François Alcover, Sep 07 2011 *)

PARI

is(n)=issquare(n^3+n^2-9*n+16) \\ Charles R Greathouse IV, Sep 06 2016

Sage

EllipticCurve([0,1,0,-9,16]).integral_points()

Extensions

Edited by Max Alekseyev, Nov 13 2009