  For $k \in \mathbb{N}$, write $S(k)$ for the largest natural number such that
there is a $k$-colouring of $\{1,\dots,S(k)\}$ with no monochromatic solution
to $x-y=z^2$. That $S(k)$ exists is a result of Bergelson, and a simple example
shows that $S(k) \geq 2^{2^{k-1}}$. The purpose of this note is to show that
$S(k)\leq 2^{2^{2^{O(k)}}}$.
