PPL 053 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
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Prize Problem LedgerErdősPPL 053Erdős Problem #30

Permanent problem IDPPL 053

Verified openErdősconjecture

Number theory

Erdős Problem #30

Let h(N) be the maximum size of a Sidon set in {1,…,N}. Is it true that, for every ε>0, h(N) = N^(1/2)+O_ε(N^ε)?

number theorysidon setsadditive combinatorics
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The problem

Let h(N) be the maximum size of a Sidon set in {1,…,N}. Is it true that, for every ε>0, h(N) = N^(1/2)+O_ε(N^ε)?

Open since1961earliest source
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$1000Paul 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

5 unique reference linksCanonical problem page Claim or award rules OEIS A143824 OEIS A227590 OEIS A003022
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Related open targets

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