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Problems · Vela Mathematics Program

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declared open · formalizederdos:203
True ↔ ∃ m, m.Coprime 6 ∧ ∀ (k l : ℕ), ¬Nat.Prime (2 ^ k * 3 ^ l * m + 1)
primescovering systemsN/A2 sources
declared open · formalizederdos:273
True ↔ ∃ c, ∀ (i : c.ι), ∃ p, Nat.Prime p ∧ 5 ≤ p ∧ c.moduli i = Ideal.span {↑(p - 1)}
number theorycovering systemsN/A2 sources
declared open · formalizederdos:274
sorry ↔ ∀ (G : Type u_1) [inst : Group G], 1 < ENat.card G → ∀ (ι : Type u_2) [inst_1 : Fintype ι] (P : Erdos274.Group.ExactCovering G ι), 1 < Fintype.card ι → ∃ i j, i ≠ j ∧ Cardinal.mk ↥(P.parts i) = Cardinal.mk ↥(P.parts j)
group theorycovering systemsN/A3 sources
declared open · formalizederdos:276
True ↔ ∃ a, Erdos276.IsLucasSequence a ∧ (∀ (k : ℕ), (a k).Composite) ∧ ∀ n > 1, ∃ k, n.gcd (a k) = 1
number theorycovering systemsN/A2 sources
declared openerdos:278
Erdős problem 278
number theorycovering systemsN/A
declared open · formalizederdos:279
True ↔ ∀ k ≥ 3, ∃ a N, (∀ (p : ℕ), Nat.Prime p → a p < p) ∧ ∀ n ≥ N, ∃ p, ∃ t ≥ k, Nat.Prime p ∧ n = a p + t * p
number theorycovering systemsprimesN/A2 sources
declared open · formalizederdos:1113
sorry ↔ ∃ k, k.IsSierpinskiNumber ∧ ¬Erdos1113.HasFinitePrimeCoveringSet k
number theorycovering systemsA0763362 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

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