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Problems · Vela Mathematics Program

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declared solved · formalized · $100erdos:119
For unit-modulus complex numbers ziz_i, let pn(z)=∏i≤n(z−zi)p_n(z)=\prod_{i\le n}(z-z_i) and Mn=max⁡∣z∣=1∣pn(z)∣M_n=\max_{|z|=1}|p_n(z)|. Erdős's prize question: is there c>0c>0 with ∑k≤nMk>n1+c\sum_{k\le n} M_k > n^{1+c}?
analysispolynomialsN/A4 sources
declared solved · formalizederdos:318
∃ A, A.HasPosDensity ∧ ¬Erdos318.P₁ A
number theoryunit fractionsN/A2 sources
declared solved · formalizederdos:321
What is the largest A⊆{1,…,N}A\subseteq\{1,\dots,N\} such that all subset sums ∑n∈S1/n\sum_{n\in S}1/n (over S⊆AS\subseteq A) are distinct?
number theoryunit fractionsA384927 · A3915923 sources
declared solved · formalizederdos:387
False ↔ ∃ c, 0 < c ∧ ∀ (n k : ℕ), 1 ≤ k → k < n → ∃ d, ↑d ∈ Set.Ioc (c * ↑n) ↑n ∧ d ∣ n.choose k
number theorybinomial coefficientsN/A2 sources
declared solved · formalizederdos:587
∃ O > 0, ∃ O' > 0, ∀ᶠ (N : ℕ) in Filter.atTop, ↑(Erdos587.MaxNotSqSum N) ≤ O' * Real.nthRoot 3 ↑N * Real.log ↑N ^ O
number theoryA3720402 sources
declared solved · formalized · $25erdos:633
∀ {n : ℕ} {T : Affine.Triangle ℝ (EuclideanSpace ℝ (Fin 2))}, Erdos633.IsCuttable n T → n ≠ 0
geometryN/A2 sources
declared solved · formalizederdos:868
False ↔ ∀ (A : Set ℕ), A.IsAsymptoticAddBasisOfOrder 2 → Filter.Tendsto (fun n => Erdos868.ncard_add_repr A 2 n) Filter.atTop Filter.atTop → ∃ B ⊆ A, B.IsAsymptoticAddBasisOfOrder 2 ∧ ∀ b ∈ B, ¬(B \ {b}).IsAsymptoticAddBasisOfOrder 2
number theoryadditive basisN/A3 sources
declared solved · formalizederdos:888
(fun n => ↑(Nat.findGreatest (Erdos888.p n) n)) =Θ[Filter.atTop] fun n => ↑n * Real.log (Real.log ↑n) / Real.log ↑n
number theorysquaresA3875845 sources
declared solved · formalizederdos:920
True ↔ ∀ k ≥ 4, ∃ c > 0, (fun n => ↑n ^ (1 - 1 / (↑k - 1)) / Real.log ↑n ^ c) =O[Filter.atTop] fun n => ↑(Erdos920.f k n)
graph theorychromatic numberpossible2 sources