What are the subfields of $F_2[x] / (x^3 + x + 1)$? I know $F_2$ is a subfield, and so is itself, but I'm not sure if there are any more.
Thanks!
2026-04-04 10:17:09.1775297829
Subfields of $F_2[x] / (x^3 + x + 1)$
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Subfileds of any finite field of order $p^n$ are exactly of order $p^r$ where $r$ divides $n$.You may see it here:Subfields of finite fields. Now can you conclude?