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Jan 1, 2015 at 17:48 comment added alpoge Yep! Indeed. It's also the reason I'd wanted the count mod $p$ in the first place, incidentally.
Jan 1, 2015 at 17:42 comment added Noam D. Elkies I suspect that this is basically the same argument that Will Sawin gave, because the Chevalley(-Warning) congruence is also proved by summing the $(p-1)$st power and expanding.
Jan 1, 2015 at 17:38 history answered alpoge CC BY-SA 3.0