A Maximal Extension of the Best-Known Bounds for the Furstenberg-Sárközy Theorem

Alex Rice

We show that if $h\in \mathbb{Z}[x]$ is a polynomial of degree $k\ge 2$ such that $h(\mathbb{N})$ contains a multiple of $q$ for every $q\in \mathbb{N}$, known as an $\textit{int…