Erdős Problem #1190

The problem

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.

Estimate $\epsilon_m$.

Statement quoted from erdosproblems.com/1190, maintained by Thomas Bloom. Original source: [Er80,p.96]. Current status there: solved (Lean).

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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