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.References
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Additional Information
- Tamiru Jarso
- Affiliation: Mathematical Sciences Institute, The Australian National University, ACT 0200, Australia
- Email: tamiru.jarso@anu.edu.au
- Tim Trudgian
- Affiliation: School of Physical, Environmental and Mathematical Sciences, UNSW Canberra, Australia
- MR Author ID: 909247
- Email: t.trudgian@adfa.edu.au
- 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.
- © Copyright 2018 American Mathematical Society
- Journal: Math. Comp. 88 (2019), 1251-1260
- MSC (2010): Primary 11A07; Secondary 11N35, 11N69
- DOI: https://doi.org/10.1090/mcom/3378
- MathSciNet review: 3904145