OFFSET
1,1
COMMENTS
This equation gives the elliptic curve (W46) studied by Stroeker and de Weger. This curve has rank 3 with generators P1 = (25, 112), P2 = (-20, 112) and P3 = (70, 562). The list gives all integer points with y > 0 in this curve.
Each positive y corresponds to a negative solution -y - 1, so that the sequence gives all y values of solutions.
Some y values corresponds to three solutions. For y = 87, we have x = -25, 5 or 20. For y = 112, we have x = -20, -5 or 25. Any other value of y corresponds to a unique solution.
LINKS
Roelof J. Stroeker and Benjamin M. M. de Weger, Elliptic binomial diophantine equations, Math. Comp. 68 (1999), 1257-1281.
EXAMPLE
a(1) = 31: (-29)^3 - 525 * (-29) + 10156 = 996 = 31 * 32.
PROG
(SageMath) EllipticCurve([0, 0, 1, -525, 10156]).integral_points()
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Tomohiro Yamada, Jul 20 2018
STATUS
approved