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On the smallest simultaneous power nonresidue modulo a prime

  • Kevin Ford , Moubariz Z. Garaev EMAIL logo and Sergei V. Konyagin
From the journal Forum Mathematicum

Abstract

Let p be a prime and let p1,,pr be distinct prime divisors of p-1. We prove that the smallest positive integer n which is a simultaneous p1,,pr-power nonresidue modulo p satisfies

n<p1/4-cr+o(1)(p)

for some positive cr satisfying cr=e-(1+o(1))r as r.

MSC 2010: 11A15; 11A07; 11N29

Communicated by Jan Bruinier


Award Identifier / Grant number: DMS-1201442

Award Identifier / Grant number: DMS-1501982

Award Identifier / Grant number: 14-01-00332

Funding statement: The first author is supported in part by the National Science Foundation grants DMS-1201442 and DMS-1501982. The third author is supported by grant RFBR 14-01-00332.

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Received: 2015-12-7
Revised: 2016-5-16
Published Online: 2016-9-14
Published in Print: 2017-3-1

© 2017 by De Gruyter

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