On additive decompositions of primitive elements in finite fields

TL;DR

This paper investigates how primitive elements in finite fields can be expressed as sums of other elements, improving existing bounds and providing new insights into their additive decompositions.

Contribution

It refines previous bounds on additive decompositions of primitive elements in finite fields, advancing understanding in this area.

Findings

Improved bounds on additive decompositions of primitive elements

Enhanced understanding of the structure of primitive elements in finite fields

Refined mathematical techniques for analyzing finite field elements

Abstract

In this paper, we study several topics on additive decompositions of primitive elemements in finite fields. Also we refine some bounds obtained by Dartyge and S\'{a}rk\"{o}zy and Shparlinski.