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A193524 a(n)=Number of integer solutions of quartic elliptic curve y^2 = 5x^4 + 4n. 8
5, 0, 0, 3, 4, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 5, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 5, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Quintic trinomial x^5-nx+m  is reducible into cubic and quadratic factors if and only a(n)<>0.

Particular case for n=1 x^5-x+m have 3 solutions for m<>0 see A179106. Rest two (5-3) giving m=0.

LINKS

Table of n, a(n) for n=1..86.

PROG

(MAGMA) [IntegralQuarticPoints([5, 0, 0, 0, 4*n]) : n in [1..50]];

CROSSREFS

Sequence in context: A316480 A099224 A136598 * A300237 A105077 A073231

Adjacent sequences:  A193521 A193522 A193523 * A193525 A193526 A193527

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jul 29 2011

STATUS

approved

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Last modified June 13 14:01 EDT 2021. Contains 344999 sequences. (Running on oeis4.)