Concepedia

Primitive Root Theorem

The Primitive Root Theorem is a fundamental result in number theory that establishes the conditions under which a finite multiplicative group of integers modulo n admits a primitive root, thereby guaranteeing the existence of a generator for the group when n is 1, 2, 4, p^k, or 2p^k, where p is an odd prime and k is a positive integer.

67

Publications

2.8K

Citations

83

Authors

59

Institutions

Publications per year

2017–2026

1

Variants

Gauss's Primitive Root Theorem

Parents

Publications

67

Discrete Fourier transforms when the number of data samples is prime

Charles M. Rader · Proceedings of the IEEE · 1968 · 538 citations

, , +13

ARTIN'S CONJECTURE FOR PRIMITIVE ROOTS

D. R. Heath‐Brown · The Quarterly Journal of Mathematics · 1986 · 286 citations

, , +15

Primitive ideals and orbital integrals in complex classical groups

Dan Barbasch, David A. Vogan · Mathematische Annalen · 1982 · 193 citations

, , +9

Primitive normal bases for finite fields

H. W. Lenstra, René Schoof · Mathematics of Computation · 1987 · 128 citations · Full text

, , +7

Coding the Lehmer pseudo-random number generator

William H. Payne, John Rabung, T. P. Bogyó · Communications of the ACM · 1969 · 123 citations · Full text

, , +15

1–5 of 67

Authors

83

  1. LC
    L. Carlitz

    Duke University, United States

    4 publications · 145 citations

    4

    h-index

  2. AZ
    Alexandru Zaharescu

    University of Illinois Urbana-Champaign, United States

    4 publications · 68 citations

    4

    h-index

  3. PM
    Pieter Moree

    Max Planck Institute for Mathematics, Germany

    3 publications · 100 citations

    3

    h-index

  4. KS
    Kenneth S. Williams

    Carleton University, Canada

    2 publications · 48 citations

    2

    h-index

  5. HW
    H. W. Lenstra

    University of California, Berkeley, United States

    2 publications · 157 citations

    2

    h-index

1–5 of 83

Institutions

59

  1. Max Planck Institute for Mathematics

    Bonn, Germany

    3 h-index

    3 publications

    71 citations

  2. McGill University

    Montreal, Canada

    3 h-index

    4 publications

    124 citations

  3. Princeton University

    Princeton, United States

    2 h-index

    3 publications

    60 citations

  4. University of Glasgow

    Glasgow, United Kingdom

    2 h-index

    2 publications

    41 citations

  5. Polish Academy of Sciences

    Warsaw, Poland

    2 h-index

    2 publications

    22 citations

  6. Tel Aviv University

    Tel Aviv, Israel

    2 h-index

    2 publications

    109 citations

  7. Leiden University

    Leiden, The Netherlands

    2 h-index

    3 publications

    83 citations

  8. Romanian Academy

    Bucharest, Romania

    2 h-index

    4 publications

    52 citations

1–8 of 59

Venues

  1. Mathematics of Computation

    MCOM · 9 publications · 261 citations

    9

    h-index

  2. Journal of Number Theory

    4 publications · 102 citations

    4

    h-index

  3. Transactions of the American Mathematical Society

    TRAN · 4 publications · 124 citations

    4

    h-index

  4. Canadian Journal of Mathematics

    3 publications · 54 citations

    3

    h-index

  5. The Quarterly Journal of Mathematics

    3 publications · 368 citations

    3

    h-index

1–5