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Let $n$ be a nonzero integer. I am interested in the integer solutions $(x, y)$ to the equation $y^2 = x^3 + n$. Let $S$ be the set of all integer solutions $(x, y)$ to this equation.

I am wondering is there any upper bound on the size of $S$ [depend on $|n|$], and is there any algorithm [or code] to obtain the set $S$ for given $n$? Thank you for reading this post.

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    $\begingroup$ J. GEBEL, A. PETHO ̈ and H. G. ZIMMER. On Mordell’s equation. Compositio Math. 110 (1998), no. 3, 335–367. $\endgroup$
    – Felipe Voloch
    Commented Jun 12 at 7:34
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    $\begingroup$ The answers to this question discusses how to compute it for a given $n$. $\endgroup$
    – Chris Wuthrich
    Commented Jun 12 at 11:10
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    $\begingroup$ See also en.wikipedia.org/wiki/Mordell_curve $\endgroup$
    – Max Alekseyev
    Commented Jun 12 at 13:56
  • $\begingroup$ Thanks for all of you! Your comments are very helpful to me! $\endgroup$
    – lolipop
    Commented Jun 13 at 4:59

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