The board / number theory / #531
Erdős Problem #531
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Prizenone
Topicsnumber theory, ramsey theory
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Verified \(F(1)=1\), \(F(2)=9\), and certificate-backed \(F(3)=54\); an explicit checked colouring proves \(F(4)\geq201\), while the asymptotic tower-versus-double-exponential gap remains open.
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