Multivariate Polynomial Values in Difference Sets

John R. Doyle, Alex Rice

For $\ell \ge 2$ and $h\in \mathbb{Z}[x_1,\dots ,x_{\ell }]$ of degree $k\ge 2$, we show that every set $A\subseteq \{1,2,\dots ,N\}$ lacking nonzero differences in $h(\mathbb{Z}^{\e…