I've read the proof in my textbook, but it eventually boils down to contradiction, and in most cases the downside to proof by contradiction is that it removes some intuition. I also couldn't find any other explanation online! Can anyone give me an intuitive explanation as to why finite fields are of order $p^n$? I think this is a super cool fact, but I find it kind of hard to appreciate when I don't have the big picture in mind.
2026-04-06 13:49:19.1775483359
Why must the order of a finite field be the power of a prime?
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