This is a preview of subscription content, log in via an institution to check access.
References
P. Csikvári, K. Gyarmati and A. Sárközy: Density and Ramsey type results on algebraic equations with restricted solution sets, Combinatorica 32 (2012), 425–449.
K. Cwalina and T. Schoen: Tight bounds on additive Ramsey-type numbers, preprint (2015).
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.
P. Frankl, R. Graham and V. Rödl: Quantitative Theorems for Regular Systems of Equations, Journal of Combinatorial Theory 47 (1988), 246–261.
B. Green and T. Sanders: Monochromatic sums and products, Discrete Analysis 5 (2016), 1–43.
S. Lindqvist: The equation x+y =z 2 is not partition regular over Z=p nZ, http: //people.maths.ox.ac.uk/lindqvist/notes/counterex.pdf.
J. Schur: Über die Kongruenz x m+y m≡z m (mod p), Jahresber. Deutschen Math. Verein. 25 (1916), 114–117.
T. Tao and V. Vu: Additive Combinatorics, Cambridge University Press, 2010.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lindqvist, S. Partition Regularity of Generalised Fermat Equations. Combinatorica 38, 1457–1483 (2018). https://doi.org/10.1007/s00493-017-3654-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00493-017-3654-4