

A356707


Number of integral solutions to Mordell's equation y^2 = x^3 + n^3 with y positive.


7



2, 3, 0, 2, 0, 0, 1, 4, 2, 2, 1, 0, 0, 2, 0, 2, 0, 3, 0, 0, 1, 1, 1, 0, 2, 1, 0, 2, 0, 0, 0, 4, 2, 1, 1, 2, 2, 1, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 2, 3, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 1, 2, 8, 0, 0, 0, 0, 2, 1, 4, 0, 1, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 0, 3, 1, 2
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OFFSET

1,1


COMMENTS

Equivalently, number of different values of x in the integral solutions to the Mordell's equation y^2 = x^3 + n^3 apart from the trivial solution (n,0).


LINKS



FORMULA



EXAMPLE

a(2) = 3 because the solutions to y^2 = x^3 + 2^3 with y > 0 are (1,3), (2,4), and (46,312).


PROG

(SageMath) [(len(EllipticCurve(QQ, [0, n^3]).integral_points(both_signs=True))1)/2 for n in range(1, 61)] # Lucas A. Brown, Sep 03 2022


CROSSREFS



KEYWORD

nonn,hard


AUTHOR



EXTENSIONS

Offset and a(21) corrected and a(22)a(60) by Lucas A. Brown, Sep 03 2022


STATUS

approved



