I am trying to find any reference about the solutions of the Diophantine equation $x^2\pm iy^2=z^3$. It seems to me that I read about this somewhere before, but I can't remember where.
Any bibliographic reference is very welcome!
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2For each $X,Y\in \Bbb{Z}[i]$ coprime, factoring $X^2+iY^2$ you can easily find the set of $w\in \Bbb{Z}[i]$ such that $(wX)^2+i(wY)^2$ is a cube, and obtain all the solutions this way. – reuns Jan 01 '22 at 02:25
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https://math.stackexchange.com/questions/3108198/given-prime-p-find-solutions-to-x2-p-y2-z3/3108394#3108394 – individ Jan 02 '22 at 04:42