Author

Konstantinos Tsinas

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Preprint Sep 2026

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

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 set of positive density contains configurations $\{x,x+P(y),xy^s\}$ for arbitrarily large $x>y\geq 2$. This provides a density strengthening...

F. Richter, Konstantinos Tsinas · 0 citations

Preprint Sep 2026

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

Fix $s\in\mathbb{N}$. We prove that there exists a subadditive density on $\mathbb{N}$ such that, for every polynomial $P\in\mathbb{Z}[y]$ with $P(0)=0$, every set of positive density contains configurations $\{x,x+P(y),xy^s\}$ for arbitrarily large $x>y\geq 2$. When $s=1$, this strengthens Moreira's partition-regulari...

F. Richter, Konstantinos Tsinas · 0 citations