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Problems · Vela Mathematics Program

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declared disproved · formalized · $100erdos:43
If Sidon sets A,B⊆{1,…,N}A, B \subseteq \{1, \dots, N\} satisfy (A−A)∩(B−B)={0}(A-A) \cap (B-B) = \{0\}, must (∣A∣2)+(∣B∣2)≤(f(N)2)+O(1)\binom{|A|}{2} + \binom{|B|}{2} \le \binom{f(N)}{2} + O(1), where f(N)f(N) is the largest Sidon-set size in [N][N] - and can the bound be improved by a fixed proportion when ∣A∣=∣B∣|A| = |B|?
number theorysidon setsadditive combinatoricsA143824 · A227590 · A003022 · possible4 sources
declared disprovederdos:441
Erdős problem 441
number theoryA0685092 sources
declared disprovederdos:543
Erdős problem 543
number theorygroup theorypossible3 sources
declared disprovederdos:960
Erdős problem 960
geometrypossible3 sources
declared disproved · formalizederdos:1092
False ↔ (fun n => ↑n) =o[Filter.atTop] fun n => ↑(Erdos1092.f 2 n)
geometrychromatic numberN/A5 sources