Concepedia

Power Residues

Power Residues is a number-theoretic concept referring to an integer that is congruent to a perfect power modulo a given integer, specifically distinguishing those residues that arise from the solvability of congruences of the form \( x^n \equiv a \pmod{m} \) for fixed exponents \( n \) and modulus \( m \).

26

Publications

762

Citations

27

Authors

12

Institutions

Publications per year

2017–2026

0

Variants

N-th Power Residues

Parents

Publications

26

Reciprocity laws: from Euler to Eisenstein

Choice Reviews Online · 2001 · 175 citations

, , +16

On Residue Difference Sets

Emma Lehmer · Canadian Journal of Mathematics · 1953 · 86 citations · Full text

, , +6

Abelian binomials, power residues and exponential congruences

Andrzej Schinzel · Acta Arithmetica · 1977 · 56 citations · Full text

, , +11

The Spectrum of Multiplicative Functions

Andrew Granville, K. Soundararajan · Annals of Mathematics · 2001 · 56 citations

, , +8

On Euler's criterion

Emma Lehmer · Journal of the Australian Mathematical Society · 1959 · 35 citations · Full text

, , +5

1–5 of 26

Authors

27

  1. EL
    Emma Lehmer

    University of California, Berkeley, United States

    7 publications · 211 citations

    7

    h-index

  2. DH
    D. H. Lehmer

    University of California, Berkeley, United States

    3 publications · 63 citations

    3

    h-index

  3. AS
    Andrzej Schinzel

    Institute of Mathematics, Poland

    2 publications · 71 citations

    2

    h-index

  4. IG
    Irving Gerst

    Stony Brook University, United States

    1 publications · 20 citations

    1

    h-index

  5. PL
    Philip Leonard

    Carleton University, Canada

    1 publications · 14 citations

    1

    h-index

1–5 of 27

Institutions

12

  1. University of California, Berkeley

    Berkeley, United States

    2 h-index

    3 publications

    87 citations

  2. Yale University

    New Haven, United States

    2 h-index

    3 publications

    82 citations

  3. University of Manchester

    Manchester, United Kingdom

    2 h-index

    5 publications

    108 citations

  4. Arizona State University

    Tempe, United States

    1 h-index

    2 publications

    28 citations

  5. Macquarie University

    Sydney, Australia

    1 h-index

    1 publications

    12 citations

  6. University of Nottingham

    Nottingham, United Kingdom

    1 h-index

    1 publications

    14 citations

  7. The University of Texas at Austin

    Austin, United States

    1 h-index

    1 publications

    12 citations

  8. Lake Forest College

    Lake Forest, United States

    1 h-index

    1 publications

    16 citations

1–8 of 12

Venues

  1. Acta Arithmetica

    4 publications · 102 citations

    4

    h-index

  2. Canadian Journal of Mathematics

    3 publications · 142 citations

    3

    h-index

  3. Mathematics of Computation

    MCOM · 2 publications · 29 citations

    2

    h-index

  4. Proceedings of the American Mathematical Society

    PROC · 2 publications · 38 citations

    2

    h-index

  5. American Mathematical Monthly

    1 publications · 14 citations

    1

    h-index

1–5