An Additive Characterization of Fibers of Characters on F p

Abstract

Let p be an odd prime, and χ a character on F∗p of order n. We show that a partition A1 ∪ A2 ∪ · · · ∪ An of {1, 2,..., p − 1} is the partition by fibers of χ if and only if the Ai satisfy certain additive properties.

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