Quadratic non-residues that are not primitive roots

Jarso, Tamiru; Trudgian, Tim

doi:10.1090/mcom/3378

Quadratic non-residues that are not primitive roots
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by Tamiru Jarso and Tim Trudgian HTML | PDF

Math. Comp. 88 (2019), 1251-1260 Request permission

Abstract:

We prove that any prime $p$ satisfying $\phi (p-1)\leq (p-1)/4$ contains two consecutive quadratic non-residues modulo $p$ neither of which is a primitive root modulo $p$. This improves on results by Luca et al. and Gun et al.

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