Title

A Sárközy theorem for finite fields

Abstract

A classical result of Sárközy states that, for any k∈ ℕ and any positive density subset E of ℕ, there exist elements x and y of E and n ≠ 0 such that x -y = nk. A version of this result for finite fields is derived from a recent theorem of P. Larick, a short proof of which is also given.

Publication Title

Combinatorics Probability and Computing

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