OFFSET
1,1
COMMENTS
Bremner and Tzanakis showed that the list of solutions is complete.
The elliptic curve given by this equation has rank 2 over the rationals with generators (1, 2) and (2, 2).
Since there exist two integer points (x, y) and (x, -y) for each x in the sequence (we can easily see that y <> 0 for such an x), this elliptic curve has exactly 26 integer points.
LINKS
Andrew Bremner and Nicholas Tzanakis, Integer points on y^2 = x^3 - 7x + 10, Math. Comp. 41 (1983), 731-741.
Robin Hartshorne, Algebraic Geometry, GTM 52, Springer-Verlag, Chapter IV, Exercise 4.18.
PROG
(SageMath) EllipticCurve([0, 0, 0, -7, 10]).integral_points()
CROSSREFS
KEYWORD
sign,fini,full
AUTHOR
Tomohiro Yamada, Jul 04 2018
STATUS
approved