Erdős Problem #1202

The problem

Let $\epsilon,\eta>0$. Does there exist a $k$ such that, given any set of $k$ primes $p_1<\cdots<p_k<n^{1-\epsilon}$, each with a set $A_i$ of $\frac{p_i-1}{2}$ many congruence classes modulo $p_i$, the number of $m\leq n$ such that $m\not\in A_i\pmod{p_i}$ for all $i$ is at most $\epsilon n$?

Statement quoted from erdosproblems.com/1202, maintained by Thomas Bloom. Original source: [Er80,p.107]. Current status there: solved.

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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