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Erdős problem 52

Let AA be a finite set of integers. Is it true that for every ϵ>0\epsilon>0 max⁡(∣A+A∣,∣AA∣)≫ϵ∣A∣2−ϵ?\max( \lvert A+A\rvert,\lvert AA\rvert)\gg_\epsilon \lvert A\rvert^{2-\epsilon}?

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No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/52.lean

Formal Conjectures

FormalConjectures/ErdosProblems/52.leanErdos52.erdos_521 lineExact file
True ↔ ∀ (ε : ℝ), 0 < ε → ε < 1 → ∃ C, 0 < C ∧ ∀ (A : Finset ℤ), max ↑(A + A).card ↑(A * A).card ≥ C * ↑A.card ^ (2 - ε)
OpenStatement only, no proof

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

  • AI standalone

    Erdős AI contributions wiki · 3 Jun, 2026

    Machine
    Claude Mythos
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  • AI collaborating with humans

    Erdős AI contributions wiki · 28 May, 2026

    Machine
    GPT-5.5 Pro
    People
    Thomas Bloom, Will Sawin, Carl Schildkraut, Dmitrii Zhelezov
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  • AI collaborating with humans

    Erdős AI contributions wiki · 4 Jun, 2026

    Machine
    GPT-5.5
    People
    Boris Alexeev
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  • AI collaborating with humans

    Erdős AI contributions wiki · 28 May, 2026

    Machine
    GPT-5.5
    People
    Ingo Althöfer
    Open the source record

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