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 statement5 of 5

The work of de la Bretèche, Ford, and Vandehey [BFV13] implies $L(m)^{-1+o(1)}< \epsilon_m < L(m)^{-\sqrt{3}/2+o(1)},$ where $L(m)=\exp(\sqrt{\log m\log\log m})$ . The upper bound follows immediately from their upper bound as reported in [202] and partial summation.

FormalConjectures/ErdosProblems/1190.leanErdos1190.erdos_1190.variants.upper_bound1 lineExact file

1∀ (ε : ℝ), 0 < ε → ∀ᶠ (m : ℕ) in Filter.atTop, Erdos1190.eps m < scaleL m ^ (-(√3 / 2) + ε)

SolvedStatement only, no proof

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