A193524 a(n)=Number of integer solutions of quartic elliptic curve y^2 = 5x^4 + 4n.

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.

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