Pick one.

theorem erdos_194 : answer(False) ↔ ∀ k ≥ 3, ∀ r : ℝ → ℝ → Prop, IsStrictTotalOrder ℝ r → ∃ s : List ℝ, s.IsAPOfLength k ∧ (s.Pairwise r ∨ s.Pairwise (flip r))

theorem erdos_275 (r : ℕ) (a : Fin r → ℤ) (n : Fin r → ℕ) (H : ∃ k : ℤ, ∀ x ∈ Ico k (k + 2 ^ r), ∃ i, x ≡ a i [ZMOD n i]) (x : ℤ) : ∃ i, x ≡ a i [ZMOD n i]

theorem erdos_277 : answer(True) ↔ ∀ c : ℝ, ∃ n : ℕ, (σ 1 n : ℝ) > c * n ∧ ∀ (m : StrictCoveringSystem ℤ), ∃ i, (n : ℤ) ∉ m.moduli i

theorem erdos_31 : ∀ A : Set ℕ, A.Infinite → ∃ B : Set ℕ, B.HasDensity 0 ∧ ∀ᶠ n in atTop, n ∈ A + B

theorem erdos_437 : answer(True) ↔ ∀ ε : ℝ, 0 < ε → ∀ᶠ x : ℕ in atTop, (x : ℝ) ^ (1 - ε) < L x

theorem erdos_438 : Tendsto (fun N : ℕ ↦ (extremalSize N : ℝ) / (N : ℝ)) atTop (𝓝 ((11 : ℝ) / 32))

theorem erdos_482 : (∀ n : ℕ, 1 ≤ n → (a (2 * n + 1) : ℤ) - 2 * a (2 * n - 1) = (Real.digits (√2 / 2) 2 (n - 1) : ℕ)) ∧ Real.ofDigits (Real.digits (√2 / 2) 2) = √2 / 2

theorem erdos_484 : ∃ c : ℝ, 0 < c ∧ ∀ k : ℕ, 0 < k → ∃ N₀ : ℕ, ∀ N : ℕ, N₀ ≤ N → ∀ f : ℕ → Fin k, c * N ≤ (((Finset.Icc 1 N).filter fun n => ∃ a ∈ Finset.Icc 1 N, ∃ b ∈ Finset.Icc 1 N, a ≠ b ∧ f a = f b ∧ a + b = n).card : ℝ)

theorem erdos_519 : answer(True) ↔ ∃ c : ℝ, 0 < c ∧ ∀ (n : ℕ) (hn : 0 < n) (z : Fin n → ℂ), z ⟨0, hn⟩ = 1 → ∃ k : Fin n, c < ‖powerSum z (k.val + 1)‖

theorem erdos_645 (c : ℕ → Bool) : ∃ x d, 0 < x ∧ x < d ∧ (∃ C, c x = C ∧ c (x + d) = C ∧ c (x + 2 * d) = C)

theorem erdos_646 : answer(True) ↔ ∀ S : Finset ℕ, (∀ p ∈ S, p.Prime) → {n : ℕ | ∀ p ∈ S, Even (padicValNat p (n !))}.Infinite

theorem erdos_690 : answer(False) ↔ ∀ k ≥ 1, ∀ d : ℕ → ℝ, (∀ p, p.Prime → (kthPrimeFactorSet k p).HasDensity (d p)) → IsUnimodalOnPrimes d

theorem erdos_728 : answer(True) ↔ ∀ᶠ ε : ℝ in 𝓝[>] 0, ∀ C > (0 : ℝ), ∀ C' > C, ∃ a b n : ℕ, 0 < n ∧ ε * n < a ∧ ε * n < b ∧ a ! * b ! ∣ n ! * (a + b - n)! ∧ a + b > n + C * log n ∧ a + b < n + C' * log n