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A356708
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Number of integral solutions to Mordell's equation y^2 = x^3 + n^3 with y nonnegative.
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7
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3, 4, 1, 3, 1, 1, 2, 5, 3, 3, 2, 1, 1, 3, 1, 3, 1, 4, 1, 1, 2, 2, 2, 1, 3, 2, 1, 3, 1, 1, 1, 5, 3, 2, 2, 3, 3, 2, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 3, 4, 1, 1, 1, 1, 1, 4, 4, 1, 1, 1, 1, 1, 2, 3, 9, 1, 1, 1, 1, 3, 2, 5, 1, 2, 1, 1, 1, 5, 1, 1, 3, 1, 1, 3, 1, 2, 1, 3, 1, 3, 3, 2, 1, 1, 2, 1, 1, 4, 2, 3
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OFFSET
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1,1
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COMMENTS
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Equivalently, number of different values of x in the integral solutions to the Mordell's equation y^2 = x^3 + n^3.
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LINKS
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FORMULA
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EXAMPLE
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a(2) = 4 because the solutions to y^2 = x^3 + 2^3 with y >= 0 are (-2,0), (1,3), (2,4), and (46,312).
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PROG
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(SageMath) [(len(EllipticCurve(QQ, [0, n^3]).integral_points(both_signs=True))+1)/2 for n in range(1, 61)] # Lucas A. Brown, Sep 04 2022
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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