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Find all integral solutions

$x^3-9=y^2$

I tried many times but still no idea how to solve it. I will be grateful for any help.

Bart Michels
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user210745
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1 Answers1

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The elliptic curve of type $y^2=x^3-n$ is called Mordell curve. For $n=9$ it has no integral solutions, see here. Some of the cases can be solved by considering it modulo $4$, see here, for the case $x^3+7=y^2$. Note that $7\equiv -9 \bmod 4$.

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Dietrich Burde
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