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.
2026-03-25 03:07:08.1774408028
$x^3-9=y^2$ find integral solutions
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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 $7\equiv -9 \bmod 4$.