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> Suppose $m^3=n^4-4$ where $m,n \in \mathbb Z$.
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> a) Show that $m$ cannot be even if $n$ is odd.
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> b) Show that $m$ and $n$ cannot both be even.
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> c) By considering the prime factors of $m$,$n^2-2$ and $n^2+2$, show there is no integer solutions to $m^3=n^4-4$
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I can do the first two parts, but find it hard to start part c, how shall I think about this problem and where shall I start?