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Author's Draft

Monochromatic solutions to $x + y = z^2$

  • Ben Joseph Green,
    Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Rd, Oxford OX2 6GG, UK
  • Sofia Lindqvist,
    Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Rd, Oxford OX2 6GG, UK
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Abstract

Suppose that $\mathbb{N}$ is $2$-coloured. Then there are infinitely many monochromatic solutions to $x + y = z^2$. On the other hand, there is a $3$-colouring of $\mathbb{N}$ with only finitely many monochromatic solutions to this equation.
Keywords: additive combinatorics, Ramsey theory additive combinatorics, Ramsey theory
MSC Classifications: 11B75, 05D10 show english descriptions Other combinatorial number theory
Ramsey theory [See also 05C55]
11B75 - Other combinatorial number theory
05D10 - Ramsey theory [See also 05C55]
 

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