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A259191
Number of integral solutions to y^2 = x^3 + n*x^2 + n (with y nonnegative).
1
3, 0, 0, 4, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 1, 8, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 6, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 6, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0
OFFSET
1,1
COMMENTS
If n is square there are at least two solutions, corresponding to x = 0 and x = -n. If n = 2^(2k) there are at least three solutions, corresponding to x = 0, x = -2^(2k), and x = 2^(6k-2) + 2^(2k). If n = 2k^2 + 2k, there is at least one solution, corresponding to x = 1.
PROG
(Sage)
for i in range(1, 31):
E=EllipticCurve([0, i, 0, 0, i])
print(len(E.integral_points()))
CROSSREFS
Sequence in context: A363155 A364084 A288654 * A240455 A304263 A305223
KEYWORD
nonn
AUTHOR
Morris Neene, Jun 20 2015
STATUS
approved