Problem 351

Erdős Problem #351: declared status 'proved'. Formalized: yes. 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 integers? Prize: no. Tags: complete sequences, number theory.