Find all solutions (x, y in mathbb{Z}) to the following Diophantine equations: (a) (x^{2}=y^{3}). (b) (x^{2}-x=y^{3}). (c)
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Find all solutions \(x, y \in \mathbb{Z}\) to the following Diophantine equations:
(a) \(x^{2}=y^{3}\).
(b) \(x^{2}-x=y^{3}\).
(c) \(x^{2}=y^{4}-77\).
(d) \(x^{3}=4 y^{2}+4 y-3\).
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