Vela Mathematics Program: problems

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71 problems · 1/2Number SourcesGraph view

declared solved · $100erdos:54

Erdős problem 54

number theoryramsey theoryN/A

declared solved · $250erdos:55

Erdős problem 55

number theoryramsey theoryN/A

declared solved · formalized · $100erdos:119

For unit-modulus complex numbers

z_i

, let

p_n(z)=\prod_{i\le n}(z-z_i)

and

M_n=\max_{|z|=1}|p_n(z)|

. Erdős's prize question: is there

c>0

with

\sum_{k\le n} M_k > n^{1+c}

analysispolynomialsN/A4 sources

declared solvederdos:136

Erdős problem 136

graph theorypossible

declared solvederdos:186

Erdős problem 186

additive combinatoricsA389784

declared solvederdos:190

Erdős problem 190

additive combinatoricsarithmetic progressionspossible

declared solvederdos:223

Erdős problem 223

geometrydistancespossible

declared solvederdos:262

Erdős problem 262

irrationalityN/A

declared solvederdos:297

Erdős problem 297

number theoryunit fractionsA092670

declared solvederdos:300

Erdős problem 300

number theoryunit fractionsA390393

declared solved · formalizederdos:318

∃ A, A.HasPosDensity ∧ ¬Erdos318.P₁ A

number theoryunit fractionsN/A2 sources

declared solvederdos:320

Let

S(N)

count the distinct values of

\sum_{n\in A} 1/n

over

A\subseteq\{1,\dots,N\}

. Estimate

S(N)

number theoryunit fractionsA0722072 sources

declared solved · formalizederdos:321

What is the largest

A\subseteq\{1,\dots,N\}

such that all subset sums

\sum_{n\in S}1/n

(over

S\subseteq A

) are distinct?

number theoryunit fractionsA384927 · A3915923 sources

declared solvederdos:360

Erdős problem 360

number theorypossible

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 solvederdos:438

Erdős problem 438

number theoryA363069

declared solvederdos:440

Erdős problem 440

number theoryN/A

declared solvederdos:446

Erdős problem 446

number theorydivisorsA074738

declared solvederdos:482

Erdős problem 482

number theoryA004539

declared solvederdos:504

Erdős problem 504

geometryN/A

declared solvederdos:526

Erdős problem 526

probabilitygeometryN/A

declared solvederdos:534

Erdős problem 534

number theoryintersecting familyA387543 · A387698

declared solvederdos:542

Erdős problem 542

number theoryN/A

declared solvederdos:581

Erdős problem 581

graph theorypossible

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 solvederdos:603

Erdős problem 603

combinatoricsset theoryN/A3 sources

declared solvederdos:606

Erdős problem 606

geometryN/A

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 solvederdos:690

Erdős problem 690

number theorypossible4 sources

declared solvederdos:721

Erdős problem 721

number theoryadditive combinatoricsramsey theoryA171081

declared solvederdos:735

Erdős problem 735

geometryN/A

declared solvederdos:747

Erdős problem 747

combinatoricshypergraphsN/A

declared solvederdos:758

Erdős problem 758

graph theorychromatic numberpossible

declared solvederdos:759

Erdős problem 759

graph theorychromatic numberpossible

declared solvederdos:777

Erdős problem 777

graph theorycombinatoricsN/A

declared solvederdos:783

Erdős problem 783

number theoryN/A3 sources

declared solvederdos:784

Erdős problem 784

number theoryN/A

declared solvederdos:834

Erdős problem 834

graph theoryhypergraphsN/A

declared solvederdos:841

Erdős problem 841

number theoryA092487

declared solvederdos:858

Erdős problem 858

number theoryprimitive setsN/A4 sources

declared solvederdos:861

Erdős problem 861

number theorysidon setsA143824 · A227590 · A003022 · A143823

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 solvederdos:882

Erdős problem 882

number theoryprimitive setspossible

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 solvederdos:896

Erdős problem 896

number theorypossible3 sources

declared solvederdos:915

Erdős problem 915

graph theoryN/A

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

declared solvederdos:948

Erdős problem 948

number theoryramsey theoryN/A3 sources

declared solvederdos:988

Erdős problem 988

discrepancypossible

declared solvederdos:989

Erdős problem 989

discrepancypossible

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