On the Minimal Number of Small Elements Generating Finite Prime Fields

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In this note, we give an upper bound for the number of elements from the interval necessary to generate the finite field with an odd prime. The general result depends on the distribution of the divisors of and can be used to deduce results which hold for almost all primes.

Original languageEnglish
Pages (from-to)177-184
Number of pages8
JournalBulletin of the Australian Mathematical Society
Issue number2
Publication statusPublished - 1 Oct 2017



  • algorithmic number theory
  • character sum
  • generating set
  • Phrases finite field
  • primitive root
  • sieve theory

ASJC Scopus subject areas

  • Mathematics(all)

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