All Random Solved Random Open
Let $p(x)\in \mathbb{Q}[x]$. Is it true that \[A=\{ p(n)+1/n : n\in \mathbb{N}\}\] is strongly complete, in the sense that, for any finite set $B$, \[\left\{\sum_{n\in X}n : X\subseteq A\backslash B\textrm{ finite }\right\}\] contains all sufficiently large rational numbers?
Graham [Gr64f] proved this is true when $p(n)=n$. Erdős and Graham also ask which rational functions $r(x)\in\mathbb{Z}[x]$ force $\{ r(n) : n\in\mathbb{N}\}$ to be complete?