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arXiv · 1711.06392

Linear combinations of primitive elements of a finite field

Stephen Cohen·Tomás Oliveira e Silva·Nicole Sutherland·Tim Trudgian
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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 $p$.

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Stephen Cohen, Tomás Oliveira e Silva, Nicole Sutherland, Tim Trudgian. 2017-11-17. Linear combinations of primitive elements of a finite field. https://doi.org/10.1016/j.ffa.2018.02.009

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