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A193587 Numbers k such that the quartic elliptic curve y^2 = 5x^4 - 4k has integer solutions. 0
1, 4, 11, 16, 19, 20, 25, 29, 31, 45, 59, 64, 71, 79, 81, 89, 95, 99, 101, 124, 131, 139, 151, 169, 176, 179, 181, 191, 199, 211, 220, 229, 239, 245, 251, 256, 271, 275, 284, 295, 304, 311, 316, 319, 320, 324, 349, 359, 361, 369, 379, 395, 400, 401, 439, 451 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For these numbers k there exists an integer m such that the quintic trinomial x^5+k*x+m factors as a cubic times a quadratic.

Positive numbers of the form -d^4 + 3 d^2 e - e^2.

LINKS

Table of n, a(n) for n=1..56.

FORMULA

Complement to A193533.

MATHEMATICA

aa = {}; Do[Do[k = -d^4 + 3 d^2 e - e^2; If[k > 0, AppendTo[aa, k ]], {d, -100, 100}], {e, -100, 100}]; Take[Union[aa], 100]

CROSSREFS

Cf. A193524, A193528, A193531, A193533, A193584.

Sequence in context: A022131 A091391 A135105 * A261155 A248104 A072423

Adjacent sequences:  A193584 A193585 A193586 * A193588 A193589 A193590

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jul 31 2011

STATUS

approved

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Last modified April 22 11:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)