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Erdős Problem #866

Erdős problem #866 · erdosproblems.com/866

Estimate the least excess gk(N)g_k(N) forcing kk integers whose pairwise sums all lie in a dense subset of {1,,2N}\{1, \dots, 2N\}; in particular, determine the positive variant h4(n)h_4(n).

Result
Proved(see note)
Status
Partial result
AI contribution
AI-discovered
Method
Argument
Field
Additive Combinatorics
Posed by
Year posed
Years open
Solved
2026-07-08
Model
Demonstrandum multi-agent pipeline
Vendor
Collaborators
Verification
Lean-verified
Publication
Announced
Significance
10 / 100
Disclosed cost
Wikipedia
No dedicated article

What was actually shown

h₄(n) = 4 for every n ≥ 331,777, with improved global bounds; the broader problem remains open

Verification

Headline theorems Lean-checked; 298 exact finite cells independently certified.

Source

erdosproblems.com/866

Discussion