Concepedia

Catalan's Equation

Catalan's Equation is a Diophantine equation of the form \( x^a - y^b = 1 \), where \( x, y, a, b \) are integers greater than 1, distinguished by its conjecture—now proven—that the only solution in the natural numbers is \( 3^2 - 2^3 = 1 \).

34

Publications

1.1K

Citations

53

Authors

32

Institutions

Publications per year

2017–2026

4

Parents

Publications

34

Catalan Numbers, Their Generalization, and Their Uses

Peter Hilton, Jean Pedersen · The Mathematical Intelligencer · 1991 · 236 citations

, , +8

Catalan-like Numbers and Determinants

Martin Aigner · Journal of Combinatorial Theory Series A · 1999 · 114 citations

, , +7

On the equation of Catalan

R. Tijdeman · Acta Arithmetica · 1976 · 93 citations · Full text

, , +2

A combinatorial identity with application to Catalan numbers

Hao Pan, Zhi‐Wei Sun · Discrete Mathematics · 2006 · 68 citations

, , +9

ON SOME NEW CONGRUENCES FOR BINOMIAL COEFFICIENTS

Zhi‐Wei Sun, Roberto Tauraso · International Journal of Number Theory · 2011 · 62 citations

, , +9

1–5 of 34

Authors

53

  1. ZS
    Zhi‐Wei Sun

    Nanjing University, China

    4 publications · 156 citations

    4

    h-index

  2. HP
    Hao Pan

    Nanjing University, China

    3 publications · 94 citations

    3

    h-index

  3. DS
    Dae San Kim

    Sogang University, South Korea

    3 publications · 58 citations

    3

    h-index

  4. JJ
    Jayaraman Jayabharathi

    Annamalai University, India

    2 publications · 37 citations

    2

    h-index

  5. RT
    Roberto Tauraso

    University of Rome Tor Vergata, Italy

    2 publications · 72 citations

    2

    h-index

1–5 of 53

Institutions

32

  1. Nanjing University

    Nanjing, China

    4 h-index

    7 publications

    256 citations

  2. Annamalai University

    Chidambaram, India

    2 h-index

    7 publications

    138 citations

  3. Université de Strasbourg

    Strasbourg, France

    2 h-index

    2 publications

    35 citations

  4. Kwangwoon University

    Seoul, South Korea

    2 h-index

    2 publications

    39 citations

  5. Sogang University

    Seoul, South Korea

    2 h-index

    2 publications

    39 citations

  6. Jadavpur University

    Kolkata, India

    1 h-index

    3 publications

    111 citations

  7. Binghamton University

    Binghamton, United States

    1 h-index

    1 publications

    236 citations

  8. Saarland University

    Saarbrücken, Germany

    1 h-index

    1 publications

    19 citations

1–8 of 32

Venues

  1. Discrete Mathematics

    3 publications · 103 citations

    3

    h-index

  2. Journal of Combinatorial Theory Series A

    2 publications · 142 citations

    2

    h-index

  3. Acta Arithmetica

    2 publications · 112 citations

    2

    h-index

  4. 2

    h-index

  5. arXiv (Cornell University)

    Repository · 2 publications · 36 citations

    2

    h-index

1–5