On the number of monochromatic solutions of x+y=z2

Ayman Khalfalah, Endre Szemerédi

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In the present work we prove the following conjecture of Erdos, Roth, Sárközy and T. Sós: Let $f$ be a polynomial of integer coefficients such that 2|f(z) for some integer $z$. Then, for any $k$-colouring of the integers, the equation $x+y=f(z)$ has a solution in which $x$ and $y$ have the same colour. A well-known special case of this conjecture referred to the case f(z)=z2.

Original languageEnglish
Pages (from-to)213-227
Number of pages15
JournalCombinatorics Probability and Computing
Volume15
Issue number1-2
DOIs
Publication statusPublished - Jan 2006

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Number of Solutions
Coloring
Polynomials
Color
Integer
Erdös
Colouring
Polynomial
Coefficient

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Statistics and Probability

Cite this

On the number of monochromatic solutions of x+y=z2. / Khalfalah, Ayman; Szemerédi, Endre.

In: Combinatorics Probability and Computing, Vol. 15, No. 1-2, 01.2006, p. 213-227.

Research output: Contribution to journalArticle

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