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ON THE CONSECUTIVE POWERS OF A PRIMITIVE ROOT: GAPS AND EXPONENTIAL SUMS

Part of: Sequences and sets Finite fields and commutative rings (number-theoretic aspects) Elementary number theory

Published online by Cambridge University Press:  08 November 2011

Sergei V. Konyagin  and
Igor E. Shparlinski
Sergei V. Konyagin
Affiliation:
Steklov Mathematical Institute, 8 Gubkin Street, Moscow, 119991, Russia (email: konyagin23@gmail.com)
Igor E. Shparlinski
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia (email: igor.shparlinski@mq.edu.au)
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Abstract

For a primitive root g modulo a prime p≥1 we obtain upper bounds on the gaps between the residues modulo p of the N consecutive powers agn, n=1,…,N, which is uniform over all integers a with gcd (a,p)=1.

MSC classification

Secondary: 11A07: Congruences; primitive roots; residue systems 11B05: Density, gaps, topology 11B50: Sequences (mod $m$) 11T23: Exponential sums
Type
Research Article
Information
Mathematika , Volume 58 , Issue 1 , January 2012 , pp. 11 - 20
Copyright
Copyright © University College London 2012

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