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Monochromatic Solutions to
$x+y=z^{2}$
Published online by Cambridge University Press: 07 January 2019
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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- © Canadian Mathematical Society 2018
Footnotes
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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