Some negative answers to the Bergelson-Hindman's question

Qinqi Wu

Let $p_1,\dots ,p_d$ be integral polynomials vanishing at $0$. It was asked by Bergelson and Hindman whenever $A$ is large, whether the set $\{(m,n)\in \mathbb{N}^2:m+p_1(n),m+p_2(n…