Erdős problem 283 · problems.science

Let $p\colon \mathbb{Z} \rightarrow \mathbb{Z}$ be a polynomial whose leading coefficient is positive and such that there exists no $d≥2$ with $d ∣ p(n)$ for all $n≥1$ . Is it true that, for all sufficiently large $m$ , there exist integers $1≤n_1<\dots < n_k$ such that $1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}$ and $m=p(n_1)+\cdots+p(n_k)$ ?

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Formalization
Erdős AI contributions wiki · 28 Mar, 2026
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Aristotle
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Formalization
Erdős AI contributions wiki · 6 May, 2026
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Claude Opus 4.7, GPT-5.5 Pro
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AI collaborating with humans
Erdős AI contributions wiki · 3 May, 2026
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GPT-5.5 Pro
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Kevin Barreto, Liam Price
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argument
VibeMathed
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GPT-5.5 Pro
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Kevin Barreto, Liam Price
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resolved
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