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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the value set of Fermat quotients


Author: Igor E. Shparlinski
Journal: Proc. Amer. Math. Soc. 140 (2012), 1199-1206
MSC (2000): Primary 11A07, 11L07
Published electronically: August 2, 2011
MathSciNet review: 2869105
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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$.


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Additional Information

Igor E. Shparlinski
Affiliation: Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
Email: igor.shparlinski@mq.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11203-6
PII: S 0002-9939(2011)11203-6
Keywords: Fermat quotients, value set, preimage
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
Article copyright: © Copyright 2011 American Mathematical Society