The board / number theory / #394
Erdős Problem #394
OPENdatabase updated 2025-10-28
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Let \(t_k(n)\) denote the least \(m\) such that \(n\mid m(m+1)(m+2)\cdots (m+k-1).\)
Is it true that \(\sum_{n\leq x}t_2(n)\ll \frac{x^2}{(\log x)^c}\) for some \(c>0\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 6 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/394.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA344005
Original pageerdosproblems.com/394
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