

A356713


Numbers k such that Mordell's equation y^2 = x^3  k^3 has exactly 1 integral solution.


6



1, 2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 25, 27, 29, 30, 32, 33, 34, 35, 36, 37, 39, 40, 41, 43, 45, 46, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88
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OFFSET

1,2


COMMENTS

Numbers k such that Mordell's equation y^2 = x^3  k^3 has no solution other than the trivial solution (k,0).
Contains all squares: suppose that y^2 = x^3  t^6, then (y/t^3)^2 = (x/t^2)^3  1. The elliptic curve Y^2 = X^3  1 has rank 0 and the only rational points on it are (1,0), so y^2 = x^3  t^6 has only one solution (t^2,0).


LINKS



FORMULA

1 is a term since the equation y^2 = x^3  1^3 has no solution other than (1,0).


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



