Density regularity of $\{x,x+y,xy\}$ in the integers

Florian K. Richter, Konstantinos Tsinas

Fix $k,s\in \mathbb{N}$. We prove that there exists a subadditive density on $\mathbb{N}$ such that, for every polynomial $P\in \mathbb{Z}[y]$ of degree $k$ and with $P(0)=0$, every…