Linear combinations of primitive elements of a finite field

Abstract

We examine linear sums of primitive roots and their inverses in finite fields. In particular, we refine a result by Li and Han, and show that every $p>13$ has a pair of primitive roots $a$ and $b$ such that $a+b$ and $a^{-1}+b^{-1}$ are also primitive roots mod $p$.

19 pages; to appear in Finite Fields Appl