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Erdős problem 326

Does there exist A={a1<a2<⋯ }⊂NA=\{a_1<a_2<\cdots\}\subset \mathbb{N} which is a minimal basis of order 22 (every large integer is the sum of 22 elements from AA, and no proper subset of AA has this property) such that lim⁡k→∞ak/k2=c\lim_{k\to \infty}a_k/k^2=c for some c≠0c\neq 0? A claimed construction gives a minimal basis with A(x)=Cx+O(1)A(x)=C\sqrt{x}+O(1), answering the question affirmatively; Erdős and Graham had conjectured a negative answer.

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  • AI collaborating with humans

    Erdős AI contributions wiki · 20 May-14 Jun, 2026

    Machine
    Aristotle, Codex, GPT-5.5
    People
    Aron Bhalla
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  • construction

    VibeMathed

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    GPT-5.5, Aristotle, Codex
    People
    Aron Bhalla
    Reported outcome
    candidate
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