

A179419


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


4



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
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OFFSET

1,1


COMMENTS

Also positive cubes not in A179163.
Mordell curve y^2=x^3n 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.


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KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



