PPL 060 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
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Prize Problem LedgerErdősPPL 060Erdős Problem #52

Permanent problem IDPPL 060

Verified openErdősconjecture

Number theory

Erdős Problem #52

Let A be a finite set of integers. Is it true that for every ε>0 max( | A+A|,| AA|)≫_ε | A|^(2-ε)?

number theoryadditive combinatorics
01

The problem

Let A be a finite set of integers. Is it true that for every ε>0 max( | A+A|,| AA|)≫_ε | A|^(2-ε)?

Open since1977earliest source
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$250Paul Erdős / Combinatorics Foundation
Documented

A solution must appear in a reputable journal, with documentation that Erdős offered the displayed amount. Claims are administered by the Combinatorics Foundation; erdosproblems.com does not pay awards.

Award source ↗Rules ↗
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Sources & reading

3 unique reference linksCanonical problem page Claim or award rules OEIS A263996
04

Related open targets

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