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Monochromatic solutions to x + y = z^2

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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.4153/CJM-2017-036-1

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Institution:
University of Oxford
Department:
Magdalen College
Role:
Author
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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
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Funding agency for:
Green, BJ
Publisher:
Canadian Mathematical Society Publisher's website
Journal:
Canadian Journal of Mathematics Journal website
Volume:
71
Issue:
3
Pages:
579-605
Publication date:
2018-01-17
Acceptance date:
2017-08-31
DOI:
EISSN:
1496-4279
ISSN:
0008-414X
Pubs id:
pubs:725038
URN:
uri:3e1bb582-5d88-4d9c-81cc-74eb203a35af
UUID:
uuid:3e1bb582-5d88-4d9c-81cc-74eb203a35af
Local pid:
pubs:725038

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