Vela Mathematics Program: problems

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34 problemsGraph view

declared solved · $100erdos:54

Erdős problem 54

number theoryramsey theoryN/A

declared solved · $250erdos:55

Erdős problem 55

number theoryramsey theoryN/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:534

Erdős problem 534

number theoryintersecting familyA387543 · A387698

declared solvederdos:542

Erdős problem 542

number theoryN/A

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:690

Erdős problem 690

number theorypossible4 sources

declared solvederdos:721

Erdős problem 721

number theoryadditive combinatoricsramsey theoryA171081

declared solvederdos:783

Erdős problem 783

number theoryN/A3 sources

declared solvederdos:784

Erdős problem 784

number theoryN/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:948

Erdős problem 948

number theoryramsey theoryN/A3 sources

declared solvederdos:1001

Erdős problem 1001

number theorydiophantine approximationN/A

declared solvederdos:1187

Erdős problem 1187

number theoryprimesadditive combinatoricsN/A3 sources

declared solvederdos:1195

Erdős problem 1195

number theorypossible3 sources

declared solvederdos:1202

Erdős problem 1202

number theoryprimespossible3 sources

declared solvederdos:1205

Erdős problem 1205

number theorypossible

declared solvederdos:1211

Erdős problem 1211

number theoryramsey theorypossible

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