A maximal extension of the best-known bounds for the Furstenberg–Sárközy theorem
A maximal extension of the best-known bounds for the Furstenberg–Sárközy theorem
We show that if $h\in \mathbb Z[x]$ is a polynomial of degree $k\geq 2$ such that $h(\mathbb N)$ contains a multiple of $q$ for every $q\in\mathbb N$, known as an <em>intersective polynomial</em>, then any subset of $\{1,\dots,N\}$ with no nonzero differe