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Can you guys give me any hint on how to prove(or disprove): any injective endomorphism on a finite field is also surjective?

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  • $\begingroup$ An injective self-map has image the same size as the domain hence... $\endgroup$ – Adam Hughes Sep 13 '14 at 23:51
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    $\begingroup$ Hint: it has nothing to do with fields. $\endgroup$ – Seth Sep 13 '14 at 23:52
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Pretty sure this doesn't even require the endomorphism property, just a general property of injective maps from a finite set to itself. Use the pigeonhole principle.

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