The board / number theory / #886
Erdős Problem #886
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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The set of divisors of \(n\) in the interval \((n^{1/2}, n^{1/2} + n^{1/2-\epsilon})\).
Let \(\epsilon>0\). Is it true that, for all large \(n\), the number of divisors of \(n\) in \((n^{1/2},n^{1/2}+n^{1/2-\epsilon})\) is \(O_\epsilon(1)\)? Erdős attributes this conjecture to Ruzsa.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/886.Prizenone
Topicsnumber theory, divisors
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/886
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