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.

33 pages

References in corpus (1)

• The abelian arithmetic regularity lemma

Cited by in corpus (1)

• On monochromatic solutions to $x-y=z^2$