On the smallest simultaneous power nonresidue modulo a prime

Kevin Ford, Moubariz Z. Garaev, Sergei V. Konyagin

Research output: Contribution to journalArticlepeer-review


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 satisfes for some positive cr satisfying cr→∞.

Original languageEnglish (US)
Pages (from-to)347-355
Number of pages9
JournalForum Mathematicum
Issue number2
StatePublished - Mar 1 2017


  • Simultaneous power nonresidues
  • primitive roots
  • sieve methods
  • well-spaced divisors

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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