PPL 055 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
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Prize Problem LedgerErdősPPL 055Erdős Problem #40

Permanent problem IDPPL 055

Verified openErdősconjecture

Number theory

Erdős Problem #40

For what functions g(N)→ ∈fty is it true that | A∩ {1,…,N}| ≫ \frac{N^(1/2)}{g(N)} implies limsup 1_A∗ 1_A(n)=∈fty?

number theoryadditive basis
01

The problem

For what functions g(N)→ ∈fty is it true that | A∩ {1,…,N}| ≫ \frac{N^(1/2)}{g(N)} implies limsup 1_A∗ 1_A(n)=∈fty?

Open since1995earliest source
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$500Paul 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.

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Sources & reading

2 unique reference linksCanonical problem page Claim or award rules
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Related open targets

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