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Erdős problem 283

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Let p ⁣:Z→Zp\colon \mathbb{Z} \rightarrow \mathbb{Z} be a polynomial whose leading coefficient is positive and such that there exists no d≥2d≥2 with d∣p(n)d ∣ p(n) for all n≥1n≥1. Is it true that, for all sufficiently large mm, there exist integers 1≤n1<⋯<nk1≤n_1<\dots < n_k such that 1=1n1+⋯+1nk1=\frac{1}{n_1}+\cdots+\frac{1}{n_k} and m=p(n1)+⋯+p(nk)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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    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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