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Mathematics of Computation

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Quadratic non-residues that are not primitive roots

Authors: Tamiru Jarso and Tim Trudgian
Journal: Math. Comp. 88 (2019), 1251-1260
MSC (2010): Primary 11A07; Secondary 11N35, 11N69
Published electronically: September 6, 2018
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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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Additional Information

Tamiru Jarso
Affiliation: Mathematical Sciences Institute, The Australian National University, ACT 0200, Australia

Tim Trudgian
Affiliation: School of Physical, Environmental and Mathematical Sciences UNSW Canberra, Australia

Received by editor(s): October 11, 2017
Received by editor(s) in revised form: March 8, 2018
Published electronically: September 6, 2018
Additional Notes: The second author was supported by Australian Research Council Future Fellowship FT160100094.
Article copyright: © Copyright 2018 American Mathematical Society