Concepedia

Fermat-catalan Equations

Fermat-Catalan Equations is a Diophantine equation of the form \(x^p + y^q = z^r\) with positive integers \(x, y, z\) and pairwise coprime exponents \(p, q, r\) satisfying \(\frac{1}{p} + \frac{1}{q} + \frac{1}{r} < 1\), distinguished by its role in conjecturally characterizing the finite set of solutions under the generalized Fermat equation framework.

85

Publications

3.1K

Citations

117

Authors

78

Institutions

Publications per year

2017–2026

5

Variants

Fermat-catalan Conjecture

Parents

Publications

85

A note on Fermat's problem

Harold W. Kuhn · Mathematical Programming · 1973 · 333 citations

, , +2

Catalan Numbers, Their Generalization, and Their Uses

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

, , +8

Geometrical properties of the Fermat-Weber problem

Roland Durier, Christian Michelot · European Journal of Operational Research · 1985 · 152 citations

, , +6

Catalan-like Numbers and Determinants

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

, , +7

Entire solutions of Fermat type differential-difference equations

Kai Liu, Tingbin Cao, Hongzhe Cao · Archiv der Mathematik · 2012 · 111 citations

, , +5

1–5 of 85

Authors

117

  1. IN
    Ivan Niven

    University of Oregon, United States

    3 publications · 63 citations

    3

    h-index

  2. HS
    H. S. Vandiver

    University of Illinois Urbana-Champaign, United States

    3 publications · 56 citations

    3

    h-index

  3. WC
    Wenchang Chu

    University of Salento, Italy

    2 publications · 23 citations

    2

    h-index

  4. MH
    Mowaffaq Hajja

    Yarmouk University, Jordan

    2 publications · 33 citations

    2

    h-index

  5. HX
    Hong-Yan Xu

    Jingdezhen Ceramic Institute, China

    2 publications · 85 citations

    2

    h-index

1–5 of 117

Institutions

78

  1. Université de Bordeaux

    Bordeaux, France

    2 h-index

    2 publications

    25 citations

  2. Yarmouk University

    Irbid, Jordan

    2 h-index

    2 publications

    33 citations

  3. University of Salento

    Lecce, Italy

    2 h-index

    2 publications

    23 citations

  4. Institute of Mathematics, Academia Sinica

    Taipei, Taiwan

    2 h-index

    2 publications

    59 citations

  5. Kwangwoon University

    Seoul, South Korea

    2 h-index

    2 publications

    39 citations

  6. Shangrao Normal University

    Shangrao, China

    2 h-index

    2 publications

    85 citations

  7. Sogang University

    Seoul, South Korea

    2 h-index

    2 publications

    39 citations

  8. Academia Sinica

    Taipei, Taiwan

    2 h-index

    2 publications

    59 citations

1–8 of 78

Venues

  1. American Mathematical Monthly

    7 publications · 116 citations

    7

    h-index

  2. Journal of Number Theory

    4 publications · 69 citations

    4

    h-index

  3. Discrete Mathematics

    4 publications · 135 citations

    4

    h-index

  4. Journal of Combinatorial Theory Series A

    4 publications · 177 citations

    4

    h-index

  5. Mathematics Magazine

    3 publications · 47 citations

    3

    h-index

1–5