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A356720 Numbers k such that Mordell's equation y^2 = x^3 + k^3 has more than 1 integral solution. 7
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 (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 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
KEYWORD
nonn
AUTHOR
Jianing Song, Aug 24 2022
STATUS
approved

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Last modified July 24 02:45 EDT 2024. Contains 374575 sequences. (Running on oeis4.)