A179162 a(n) = least positive k such that Mordell's equation y^2 = x^3 + k has exactly n integral solutions.

6, 27, 2, 343, 12, 1, 37, 8, 24, 512, 9, 35611289, 73, 10218313, 315, 129554216, 17, 274625, 297, 17576000, 2817, 200201625, 1737

Offset: 0

Author

Artur Jasinski, Jun 30 2010

Keywords

• more
• nonn

Comments

Additional known terms: a(24)=4481, a(26)=225, a(28)=2089, a(32)=1025.

For least positive k such that equation y^2 = x^3 - k has exactly n integral solutions, see A179175.

If n is odd, then a(n) is perfect cube. [Ray Chandler]

Links

• J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Crossrefs

Cf. A054504, A081119, A179145-A179162.

Extensions

Edited and a(11), a(13), a(15), a(17), a(19), a(21) added by Ray Chandler, Jul 11 2010