PPL 054 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
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Prize Problem LedgerErdősPPL 054Erdős Problem #39

Permanent problem IDPPL 054

Verified openErdősconjecture

Number theory

Erdős Problem #39

Is there an infinite Sidon set A⊂ ℕ such that | A∩ {1…,N}| ≫_ε N^(1/2-ε) for all ε>0?

number theorysidon setsadditive combinatorics
01

The problem

Is there an infinite Sidon set A⊂ ℕ such that | A∩ {1…,N}| ≫_ε N^(1/2-ε) for all ε>0?

Open since1956earliest 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.

Award source ↗Rules ↗
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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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