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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the value set of Fermat quotients
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by Igor E. Shparlinski PDF
Proc. Amer. Math. Soc. 140 (2012), 1199-1206 Request permission

Abstract:

We obtain an upper bound $p^{463/252+o(1)}$ on the smallest $L$ such that the set of the first $L$ Fermat quotients modulo a prime $p$ represents all residues modulo $p$.
References
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Additional Information
  • Igor E. Shparlinski
  • Affiliation: Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
  • MR Author ID: 192194
  • Email: igor.shparlinski@mq.edu.au
  • Received by editor(s): December 20, 2010
  • Received by editor(s) in revised form: January 2, 2011
  • Published electronically: August 2, 2011
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2011 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1199-1206
  • MSC (2000): Primary 11A07, 11L07
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11203-6
  • MathSciNet review: 2869105