On reducible and primitive subsets of $F_p$, I

Gyarmati, Katalin and Mauduit, Christian and Sárközy, András (2013) On reducible and primitive subsets of $F_p$, I. INTEGERS. ISSN 1553-1732 (Submitted)

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Abstract

A set $A\subset \mathbb F_p$ is said to be reducible if it can be represented in the form $A=B+C$ with $B, C\subset\mathbb F_p$, $|B|, |C|\ge 2$. If there are no sets $B, C$ with these properties then $A$ is said to be primitive. First three criteria are presented for primitivity of subsets of $F_p$. Then the distance between a given set $A\subset\mathbb F_p$ and the closest primitive set is studied.

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