A132414 Integers n such that n^3 - (n + 2)^2 + n + 4 is a square.

-1, 0, 3, 4, 75

Offset: 1

Author

Mohamed Bouhamida, Nov 12 2007

Keywords

• sign
• fini
• full

Comments

n^3 - (n + 2)^2 + n + 4 = n^3 - n^2 - 3*n. The set of x values of integral solutions to the elliptic curve y^2 = n^3 - n^2 - 3*n (see Magma program) is {-1, 0, 3, 4, 75}. - Klaus Brockhaus, Nov 13 2007

Examples

			0^3 - 2^2 + 4 = 0^2, 3^3 - 5^2 + 7 = 3^2, 4^3 - 6^2 + 8 = 6^2 and 75^3 - 77^2 + 79 = 645^2.
		

Crossrefs

Cf. A005563, A028560.

Programs

Magma

P := PolynomialRing(Integers()); {x: x in Sort([ p[1] : p in IntegralPoints(EllipticCurve(n^3 - n^2 - 3*n)) ])}; /* Klaus Brockhaus, Nov 13 2007 */

SageMath

[i[0] for i in EllipticCurve([0, -1, 0, -3, 0]).integral_points()] # Seiichi Manyama, Aug 26 2019