The board / number theory / #930
Erdős Problem #930
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).
\(n\) is a perfect power if there exist natural numbers \(m\) and \(l\) such that \(1 < l\) and \(m^l = n\).
Is it true that, for every \(r\), there is a \(k\) such that if \(I_1,\ldots,I_r\) are disjoint intervals of consecutive integers, all of length at least \(k\), then \[ \prod_{1\leq i\leq r}\prod_{m\in I_i}m \] is not a perfect power?
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/930.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/930
Attempts
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The live page status is OPEN with 0 claimed proofs, but “Currently working on this problem” lists Svyable and satsun93 (accessed 2026-07-28); per the collision-avoidance gate, no mathematical attempt
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