Problem 1202

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 $\epsilon n$ ?

Source: erdosproblems.com/1202

Number theory
Primes

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SolvedDisproved

An accepted solution exists. The statement is false.

Disproved. The site labels the problem SOLVED, and its curator credits Price and GPT-5.4 Pro with a negative answer, and that credit is the acceptance evidence on the claim page (Price, 2026), from which the standing derives. The status-defining argument is not held: the manuscript behind the label is inaccessible to the corpus (an online-editor read link exposing no document), and the only fixed written form of the argument known to the corpus is an external Lean file that proves the negation of the statement, not built here. See "Current assessment".

Problem 1202

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