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declared disproved · $1000erdos:2
Erdős problem 2
number theorycovering systemsA160559
declared disprovederdos:8
Erdős problem 8
number theorycovering systemsN/A
declared disproved · $100erdos:27
Erdős problem 27
number theorycovering systemsN/A
declared disprovederdos:37
Erdős problem 37
number theoryadditive combinatoricsN/A
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:121
Erdős problem 121
number theorysquaresA028391 · A013928 · A372306 · A373319 · A372306 · A373178 · A360659 · A373114 · A143301
declared disproved · formalizederdos:253
¬∀ (a : ℕ → ℕ), 0 < a 0 → Erdos253.RepresentsAPs a → Filter.Tendsto (fun n => ↑(a (n + 1)) / ↑(a n)) Filter.atTop (nhds 1) → subsetSums (Set.range a) ∈ Filter.cofinite
number theoryN/A2 sources
declared disprovederdos:309
Erdős problem 309
number theoryunit fractionsA217693
declared disprovederdos:381
Erdős problem 381
number theorydivisorsA002182
declared disprovederdos:441
Erdős problem 441
number theoryA0685092 sources
declared disproved · formalizederdos:442
False ↔ ∀ (A : Set ℕ), Filter.Tendsto (fun x => 1 / Erdos442.Real.maxLogOne (Erdos442.Real.maxLogOne x) * ∑ n ∈ (A ∩ Set.Icc 1 ⌊x⌋₊).toFinset, 1 / ↑n) Filter.atTop Filter.atTop → Filter.Tendsto (fun x => 1 / (∑ n ∈ (A ∩ Set.Icc 1 ⌊x⌋₊).toFinset, 1 / ↑n) ^ 2 * ∑ nm ∈ (Erdos442.Set.bddProdUpper A x).toFinset, 1 / ↑(nm.1.lcm nm.2)) Filter.atTop Filter.atTop
number theoryN/A2 sources
declared disproved · formalizederdos:448
False ↔ ∀ (ε : ℝ), 0 < ε → {n | ↑(Erdos448.tauPlus n) < ε * ↑n.divisors.card}.HasDensity 1
number theorydivisorsA3974332 sources
declared disprovederdos:449
Erdős problem 449
number theorydivisorspossible
declared disprovederdos:492
Erdős problem 492
number theoryN/A
declared disprovederdos:543
Erdős problem 543
number theorygroup theorypossible3 sources
declared disprovederdos:586
Erdős problem 586
number theorycovering systemsN/A
declared disprovederdos:763
Erdős problem 763
number theoryadditive combinatoricsN/A
declared disprovederdos:764
Erdős problem 764
number theoryadditive combinatoricsN/A
declared disprovederdos:869
Erdős problem 869
number theoryadditive basisN/A
declared disprovederdos:1081
Erdős problem 1081
number theorypowerfulA076871 · A076872 · possible
declared disprovederdos:1140
Erdős problem 1140
number theorypossible

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