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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
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.
PROG
(Magma) [IntegralQuarticPoints([5, 0, 0, 0, 4*n]) : n in [1..50]];
CROSSREFS
Sequence in context: A316480 A099224 A136598 * A300237 A105077 A073231
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jul 29 2011
STATUS
approved