Erdős problem 351 · problems.science

Let $p(x) \in \mathbb{Q}[x]$ be a non-constant rational polynomial with positive leading coefficient. Is it true that $A=\{ p(n)+1/n : n \in \mathbb{N}\}$ is strongly complete, in the sense that, for any finite set $B$ , $\left\{\sum_{a \in X} a : X \subseteq A \setminus B, X \textrm{ is finite}\right\}$ contains all sufficiently large integers?

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FormalConjectures/ErdosProblems/

351.lean

Retained formal statement3 of 3

Let $p(x) = x ^ 2 \in \mathbb{Q}[x]$ . It has been shown that $A=\{ p(n)+1/n : n \in \mathbb{N}\}$ is strongly complete, in the sense that, for any finite set $B$ , $\left\{\sum_{a \in X} a : X \subseteq A \setminus B, X \textrm{ is finite}\right\}$ contains all sufficiently large integers.

FormalConjectures/ErdosProblems/351.leanErdos351.erdos_351.variants.X_sq1 lineExact file

1Erdos351.HasCompleteImage (Polynomial.X ^ 2)

SolvedStatement only, no proof

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