Erdős Problem #1197

The problem

Let $E\subset (0,\infty)$ be a set of positive measure. Is it true that, for almost all $x>0$, for all sufficiently large (depending on $x$) integers $n$ there exists an integer $r\geq 1$ such that $nx\in r\cdot E$?

Statement quoted from erdosproblems.com/1197, maintained by Thomas Bloom. Original source: [Er80,p.103]. Current status there: disproved (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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