A356720 Numbers k such that Mordell's equation y^2 = x^3 + k^3 has more than 1 integral solution.

1, 2, 4, 7, 8, 9, 10, 11, 14, 16, 18, 21, 22, 23, 25, 26, 28, 32, 33, 34, 35, 36, 37, 38, 40, 44, 46, 49, 50, 56, 57, 63, 64, 65, 70, 71, 72, 74, 78, 81, 84, 86, 88, 90, 91, 92, 95, 98, 99, 100, 104, 105, 110, 112, 114, 121, 122, 126, 128, 129, 130, 132, 136, 140, 144, 148

Offset

1,2

Comments

Numbers k such that Mordell's equation y^2 = x^3 + k^3 has solutions other than the trivial solution (-k,0).

Different from A103254, which lists k such that Mordell's equation y^2 = x^3 + k^3 has solutions with positive x (or equivalently, with nonnegative x). 71, 74, and 155 are here but not in A103254.

Cube root of A356703.

Contains all squares since A356711 does.

Links

Jianing Song, Table of n, a(n) for n = 1..85 (based on the data from A103254)

Example

71 is a term since the equation y^2 = x^3 + 71^3 has 3 solutions (-71,0) and (-23,+-588).
74 is a term since the equation y^2 = x^3 + 74^3 has 3 solutions (-74,0) and (-47,+-549).
155 is a term since the equation y^2 = x^3 + 155^3 has 3 solutions (-155,0) and (-31,+-1922).

Crossrefs

Cf. A081119, A356703, A356713, A228948, A103254. Complement of A356709.

Cf. also A356710, A356711, A356712.

Sequence in context: A285535 A342777 A173416 * A103254 A299419 A083454

Adjacent sequences: A356717 A356718 A356719 * A356721 A356722 A356723

Keyword

nonn

Author

Jianing Song, Aug 24 2022

Status

approved