The board / number theory / #887
Erdős Problem #887
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is there an absolute constant \(K\) such that, for every \(C > 0\), if \(n\) is sufficiently large then \(n\) has at most \(K\) divisors in \((n^{\frac{1}{2}}, n^{\frac{1}{2}} + C n^{\frac{1}{4}})\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/887.Prizenone
Topicsnumber theory, divisors
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/887
Attempts
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An elementary Pell-orbit construction gives infinitely many n with five divisors in the required window for every C>24 (explicitly, the whole stated orbit works for C=25), improving the live comment's
PARTIAL