I know that I can verify that $f:=X^{q^d}-X\in\mathbb F_q$ and $f'$ (the formal derivative) are coprime in order to establish $f$'s separability. Is there an easier way, in particular one that does not use the formal derivative? Thanks!
2026-04-07 08:07:24.1775549244
Separability of $X^{q^d}-X\in\mathbb F_q[X]$ for $d\in\mathbb N$
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No, the argument with the formal derivative is the easiest way.