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An elliptic curve is an algebraic curve of genus one with some additional properties. Questions with this tag will often have the top-level tags nt.number-theory or ag.algebraic-geometry. Note also the tag arithmetic-geometry as well as some related tags such as rational-points, abelian-varieties, heights. Please do not use this tag for questions related to ellipses; instead use conic-sections.
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Find the diophantine-equations $3x(x^2+2)=y^2$ integer solution [closed]
Let $x,y$ be positive integers, such that
$$3x(x^2+2)=y^2$$
since
$$3\cdot 1(1^2+2)=3\times 3=9=3^2$$
$$3\cdot 2(2^2+2)=6\cdot 6=36=6^2$$
$$24\cdot 3(24^2+2)=72\cdot 578=204^2$$
so I h …