Erdős problem 1190 · problems.science

Let $\epsilon_m=\max \sum \frac{1}{n_i}$ where the maximum is taken over all finite sequences $m<n_1<\cdots<n_k$ for which there exist congruences $a_i\pmod{n_i}$ such that no integer satisfies two such congruences.

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FormalConjectures/ErdosProblems/

1190.lean

Retained formal statement3 of 5

Erdős [Er80] seems to credit Mirsky and Newman with the result that $\epsilon_m<1$ , but gives no reference.

FormalConjectures/ErdosProblems/1190.leanErdos1190.erdos_1190.variants.lt_one5 linesExact file

1∀ (m : ℕ),2  1 ≤ m →3    ∀ (S : Finset ℕ) (a : ℕ → ℤ),4      (∀ n ∈ S, m < n) →5        (∀ n ∈ S, ∀ n' ∈ S, n ≠ n' → ¬∃ x, x ≡ a n [ZMOD ↑n] ∧ x ≡ a n' [ZMOD ↑n']) → ∑ n ∈ S, (↑n)⁻¹ < 1

SolvedStatement only, no proof

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