I have to solve the Diophantine equation $y^3=4x^2+4x+5$ where $x,y\in\mathbb{Z}$ and I have been thinking now for a long time and I have really no clue how to do this. The only hint given in the exercise was that I have to factorise it in $\mathbb{Z}[i]$. I really need more hints if I want to solve this. Thank you.
2026-03-31 15:07:59.1774969679
Solve the Diophantine equation $y^3=4x^2+4x+5$ in $x,y\in\mathbb{Z}$
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