Bounds for monochromatic solutions to $\{x+y,xy\}$

Abstract

Let $r$ be a sufficiently large positive integer, and let $N\ge \exp \exp (r^{50})$. Then any $r$-colouring of $[N]$ contains a monochromatic copy of $\{x+y,xy\}$ with $x>y>2$.

37 pages