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Problems · Vela Mathematics Program

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1,217 problems · 25/25NumberSourcesGraph view
declared open · formalizederdos:1201
Is it true that for every ϵ,η>0\epsilon,\eta>0 there exists a kk such that the density of nn for which P(n(n+1)⋯(n+k))>n1−ϵP(n(n+1)\cdots(n+k))>n^{1-\epsilon} is at least 1−η1-\eta, where P(m)P(m) is the greatest prime divisor of mm? A short argument via the Matomäki-Radziwiłł theorem establishes the lower-density version.
number theoryprimespossible4 sources
declared solvederdos:1202
Erdős problem 1202
number theoryprimespossible3 sources
declared open · formalizederdos:1203
True ↔ Filter.Tendsto Erdos1203.F Filter.atTop Filter.atTop
number theorypossible2 sources
declared openerdos:1204
Erdős problem 1204
number theoryA008407 · A023193 · A135311 · possible
declared solvederdos:1205
Erdős problem 1205
number theorypossible
declared openerdos:1206
Erdős problem 1206
number theorysidon setspossible
declared openerdos:1207
Erdős problem 1207
geometrydistancespossible
declared openerdos:1208
Erdős problem 1208
geometrydistancesA193838 · A271490 · possible2 sources
declared open · formalizederdos:1209
False ↔ ∃ f, ∀ (a : ℕ → ℕ), StrictMono a → (∀ (k : ℕ), f k ≤ a k) → (∃ n, ∀ (k : ℕ), Nat.Prime (n + a k)) → {n | ∀ (k : ℕ), Nat.Prime (n + a k)}.Infinite
number theorypossible3 sources
declared open · formalizederdos:1210
True ↔ ∃ C, ∀ (n : ℕ) (A : Finset ℕ), (∀ a ∈ A, 1 ≤ a ∧ a < n) → (∀ a ∈ A, ∀ b ∈ A, a ≠ b → a.Coprime b) → ∑ a ∈ A, 1 / (↑n - ↑a) ≤ ∑ p ∈ Finset.range n with Prime p, 1 / ↑p + C
number theorypossible2 sources
declared solvederdos:1211
Erdős problem 1211
number theoryramsey theorypossible
declared open · formalizederdos:1212
∀ {a s : ℕ}, a < s → (∀ (p : ℕ), Nat.Prime p → p ∣ a → s < a + p) → a.gcd s = 1
number theoryprimespossible2 sources
declared provederdos:1213
Erdős problem 1213
additive combinatoricspossible
declared proved · formalizederdos:1214
True ↔ ∀ (x y : ℕ), x ≥ 1 → y ≥ 1 → (∀ n ≥ 1, {p | Nat.Prime p ∧ p ∣ x ^ n - 1} = {p | Nat.Prime p ∧ p ∣ y ^ n - 1}) → x = y
number theoryN/A2 sources
declared disprovederdos:1215
Erdős problem 1215
analysisN/A
declared disprovederdos:1216
Erdős problem 1216
graph theoryramsey theorypossible
declared provederdos:1217
Erdős problem 1217
number theorydivisorsprimitive setsN/A3 sources