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declared proved · formalized · $500erdos:67
∀ (f : ℕ → ↥{-1, 1}) (C : ℝ), 0 < C → ∃ d ≥ 1, ∃ m ≥ 1, C < |∑ k ∈ Finset.Icc 1 m, ↑(f (k * d))|
discrepancyA181740 · A2376952 sources
declared open · $500erdos:161
Erdős problem 161
combinatoricsramsey theorydiscrepancyN/A2 sources
declared openerdos:162
Erdős problem 162
combinatoricsramsey theorydiscrepancyN/A
declared openerdos:176
Let N(k,ℓ)N(k, \ell) be the least NN such that every f:[N]→{−1,1}f : [N] \to \{-1, 1\} has a kk-term arithmetic progression PP with ∣∑n∈Pf(n)∣≥ℓ|\sum_{n \in P} f(n)| \ge \ell. In particular, is N(k,2)≤CkN(k, 2) \le C^k?
additive combinatoricsarithmetic progressionsdiscrepancypossible3 sources
declared openerdos:177
Erdős problem 177
discrepancyarithmetic progressionsN/A
declared proved (Lean) · formalizederdos:178
True ↔ ∀ (a : ℕ → ℕ → ℕ), (∀ (i : ℕ), StrictMono (a i)) → ∃ f, (∀ (n : ℕ), f n = 1 ∨ f n = -1) ∧ ∀ (d : ℕ), ∃ C, ∀ (m i : ℕ), i < d → |∑ j ∈ Finset.range m, f (a i j)| ≤ ↑C
discrepancyN/A5 sources
declared provederdos:255
Erdős problem 255
discrepancyN/A
declared proved · formalizederdos:987
True ↔ ∀ (x : ℕ → ℝ), (∀ (j : ℕ), x j ∈ Set.Ioo 0 1) → Filter.limsup (fun k => Erdos987.A x k) Filter.atTop = ⊤
analysisdiscrepancyN/A4 sources
declared solvederdos:988
Erdős problem 988
discrepancypossible
declared solvederdos:989
Erdős problem 989
discrepancypossible
declared provederdos:991
Erdős problem 991
discrepancyN/A
declared disprovederdos:992
Erdős problem 992
discrepancyN/A
declared disprovederdos:994
Erdős problem 994
analysisdiscrepancyN/A
declared openerdos:995
Erdős problem 995
analysisdiscrepancyN/A2 sources
declared proved (Lean) · formalizederdos:997
True ↔ ∀ (α : ℝ), ¬Erdos997.IsWellDistributed fun n => Int.fract (α * ↑(Nat.nth Nat.Prime n))
analysisdiscrepancyprimesN/A6 sources
declared solved (Lean) · formalizederdos:1028
(fun n => ↑(Erdos1028.H n)) =Θ[Filter.atTop] fun n => ↑n ^ (3 / 2)
graph theorydiscrepancypossible5 sources

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