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Nov 14, 2019 at 17:56 comment added user52817 I upvote this! We should be aware of the different definitions. You point out that for a finite field $F$ of order $q$, the two polynomial functions $x$ and $x^q$ are equal. However, viewed as functions in an extension of $F$, these polynomial functions need not be equal.
Nov 14, 2019 at 16:52 history edited David E Speyer CC BY-SA 4.0
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Nov 13, 2019 at 18:42 history answered David E Speyer CC BY-SA 4.0