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I was recently studying some Diophantine equations and the equation $x^2 - y^2 = z^3$ caught my eye.I knew that $x=(n+1)(n+2)/2$ , $y=n(n+1)/2$ , $z=(n+1)$ where $n \in \mathbb{N}$ gives a set of positive integer solutions.I wanted to obtain a different form of solution when suddenly the identity

$\{(m+t)^2 - (m-t)^2 \}(4mt)^2 = (4mt)^3$ came into my mind so I could produce $x=4mt(m+t)$ ,

$y=4mt|m-t|$ , $z=4mt$ where $m,t\in \mathbb{N}$ ; I would really like to know is this a (well) known solution? Is there any solution in other forms?

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    http://www.emis.de/journals/GM/vol13nr2/andrica/andrica.pdf2012-09-21
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    Well,thanks for the link.2012-09-21

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