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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 (list; graph; refs; listen; history; text; internal format)
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).
Cube root of A179163.
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
Jianing Song, Table of n, a(n) for n = 1..108 (using data from A179149)
FORMULA
1 is a term since the equation y^2 = x^3 - 1^3 has no solution other than (1,0).
CROSSREFS
Cf. A081120, A179163, A356709, A356720. Complement of A228948.
Sequence in context: A023775 A363235 A329296 * A032867 A031999 A023760
KEYWORD
nonn
AUTHOR
Jianing Song, Aug 23 2022
STATUS
approved

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Last modified February 24 04:32 EST 2024. Contains 370288 sequences. (Running on oeis4.)