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Monochromatic Solutions to $x+y=z^{2}$

  • Ben Joseph Green (a1) and Sofia Lindqvist (a1)
Abstract

Suppose that 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 N with only finitely many monochromatic solutions to this equation.

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This work was partially supported by a grant from the Simons Foundation (award number 376201 to Ben Green) , and the first author is supported by ERC Advanced Grant AAS 279438. We thank both organisations for their support.

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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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