The board / number theory / #1149
Erdős Problem #1149
PROVEDdatabase updated 2026-01-23
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(\alpha>0\) be a real number, not an integer. The density of integers \(n\geq 1\) for which \((n,\lfloor n^\alpha\rfloor)=1\) is \(6/\pi^2\). This is true, and was proved by Bergelson and Richter [BeRi17].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/1149.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1149
Attempts
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