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Problems · Vela Mathematics Program

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604 problems · 13/13NumberSourcesGraph view
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 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