Partition Regularity of Generalised Fermat Equations

This is a preview of subscription content, access via your institution.


  1. [1]

    P. Csikvári, K. Gyarmati and A. Sárközy: Density and Ramsey type results on algebraic equations with restricted solution sets, Combinatorica 32 (2012), 425–449.

    MathSciNet  Article  MATH  Google Scholar 

  2. [2]

    K. Cwalina and T. Schoen: Tight bounds on additive Ramsey-type numbers, preprint (2015).

    MATH  Google Scholar 

  3. [3]

    L. E. Dickson: On the congrence x n+y n+z n≡0 (mod p). Journal für die reine und angewandte Mathematik 135 (1909), 134–141.

    Google Scholar 

  4. [4]

    P. Frankl, R. Graham and V. Rödl: Quantitative Theorems for Regular Systems of Equations, Journal of Combinatorial Theory 47 (1988), 246–261.

    MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    B. Green and T. Sanders: Monochromatic sums and products, Discrete Analysis 5 (2016), 1–43.

    MathSciNet  MATH  Google Scholar 

  6. [6]

    S. Lindqvist: The equation x+y =z 2 is not partition regular over Z=p nZ, http: //

  7. [7]

    J. Schur: Über die Kongruenz x m+y mz m (mod p), Jahresber. Deutschen Math. Verein. 25 (1916), 114–117.

    Google Scholar 

  8. [8]

    T. Tao and V. Vu: Additive Combinatorics, Cambridge University Press, 2010.

    MATH  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Sofia Lindqvist.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lindqvist, S. Partition Regularity of Generalised Fermat Equations. Combinatorica 38, 1457–1483 (2018).

Download citation

Mathematics Subject Classification (2000)

  • 11B75