Erdős problem 52

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

No current result

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

FormalConjectures/ErdosProblems/52.lean

Formal Conjectures

FormalConjectures/ErdosProblems/52.leanErdos52.erdos_521 lineExact file

1True ↔ ∀ (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 by these sources. Not reviewed here.

AI standalone
Erdős AI contributions wiki · 3 Jun, 2026
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Claude Mythos
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AI collaborating with humans
Erdős AI contributions wiki · 28 May, 2026
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GPT-5.5 Pro
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AI collaborating with humans
Erdős AI contributions wiki · 4 Jun, 2026
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GPT-5.5
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Boris Alexeev
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AI collaborating with humans
Erdős AI contributions wiki · 28 May, 2026
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GPT-5.5
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Ingo Althöfer
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