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

Green, Ben Joseph ; Lindqvist, Sofia

Canadian journal of mathematics, Tome 71 (2019) no. 3, pp. 579-605

Résumé

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.

Détail

DOI : 10.4153/CJM-2017-036-1

Mots-clés : additive combinatorics, Ramsey theory

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