PPL 071 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
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Prize Problem LedgerErdősPPL 071Erdős Problem #661

Permanent problem IDPPL 071

Verified openErdősconjecture

Geometry

Erdős Problem #661

Are there, for all large n, some points x_1,…,x_n,y_1,…,y_n∈ ℝ^2 such that the number of distinct distances d(x_i,y_j) is o((n/√(log n)))?

geometrydistances
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The problem

Are there, for all large n, some points x_1,…,x_n,y_1,…,y_n∈ ℝ^2 such that the number of distinct distances d(x_i,y_j) is o((n/√(log n)))?

Open sinceUnknownunknown
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$50Paul 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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