A179419 Numbers n such that Mordell elliptic curve y^2=x^3-n has a number of integral points that is both odd and > 1.

216, 343, 1331, 12167, 13824, 17576, 21952, 29791, 54872, 74088, 85184, 103823, 157464, 166375, 226981, 250047, 592704, 753571, 778688, 857375, 884736, 970299, 1124864, 1331000, 1367631, 1404928, 1643032, 1685159, 1906624, 2628072

Offset: 1

Author

Artur Jasinski, Jul 13 2010

Keywords

• nonn

Comments

Also positive cubes not in A179163.

A000578 = Union({0}, A179163, A179419).

Mordell curve y^2=x^3-n always has at least one integral solution if n is a cube, say n=k^3, (x,y)=(k,0). If there are additional solutions, they will exist in pairs - (x,y) and (x,-y). Thus the number of solutions can be odd iff n is a cube.

Crossrefs

Cf. A000578, A179163. Cube of A228948.

Extensions

Edited and extended by Ray Chandler, Jul 14 2010