The board / number theory / #697
Erdős Problem #697
PROVEDdatabase updated 2025-12-20
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).
For each \(m\) and \(\alpha\), the density of the set of integers which are divisible by some \(d \equiv 1 \pmod{m}\) with \(1 < d < \exp (m ^ \alpha)\) exists.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/697.Prizenone
Topicsnumber theory, divisors
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/697
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.