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declared verifiable · formalizederdos:7
Can there be a finite covering system of the integers with distinct moduli, all of which are odd and greater than 11?
number theorycovering systemsN/A4 sources
declared solved (Lean) · formalizederdos:202
∃ o, o =o[Filter.atTop] 1 ∧ ∀ᶠ (N : ℕ) in Filter.atTop, ↑(Erdos202.f N) = ↑N * scaleL N ^ (-1 + o N)
covering systemsA3899756 sources
declared proved (Lean) · formalizederdos:281
True ↔ ∀ (n : ℕ → ℕ), StrictMono n → (∀ (i : ℕ), 0 < n i) → (∀ (a : Erdos281.ResidueChoice n), (Erdos281.avoidAll n a).HasIntDensity 0) → ∀ (ε : ℝ), 0 < ε → ∃ k, ∀ (a : Erdos281.ResidueChoice n), ∃ d, (Erdos281.avoidPrefix n a k).HasIntDensity d ∧ d < ε
number theorycovering systemsN/A7 sources
declared open · formalizederdos:1188
Estimate the number F(x)F(x) of minimal distinct covering systems whose moduli all lie in [1,x][1, x]. The candidate proof gives log⁡log⁡F(x)/log⁡x→1\log\log F(x)/\log x \to 1, i.e. F(x)=exp⁡(x1+o(1))F(x) = \exp(x^{1+o(1)}).
number theorycovering systemspossible4 sources
declared openerdos:1189
For irreducible covering sets of size kk, determine their count, the possible largest modulus, the maximal reciprocal sum, and whether divisor-set examples occur infinitely often.
number theorycovering systemspossible2 sources
declared solved (Lean) · formalizederdos:1190
∀ (ε : ℝ), 0 < ε → ∀ᶠ (m : ℕ) in Filter.atTop, scaleL m ^ (-1 - ε) < Erdos1190.eps m ∧ Erdos1190.eps m < scaleL m ^ (-1 + ε)
number theorycovering systemspossible6 sources

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