There's quite a lot of literature about how to find a generator of the multiplicative subgroup of a finite field $\mathbb{F}$.
A much simpler question: can we find an additive generator $a$? So that $\{ a, a + a, a + a + a, ...\} = \mathbb{F}$?
2026-04-06 01:51:51.1775440311
Finding an additive generator of a finite field
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The question is equivalent to asking whether a finite field is a cyclic additive group.
Finite prime fields are cyclic additive groups. Extension fields are not.