Source labels openChecked July 26, 2026

Erdős Problem 930

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?

Number theory AMS 11

Mathematical statement

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 source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_930

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_930 :    answer(sorry) ↔ ∀ r > 0, ∃ k, ∀ I₁ I₂ : Fin r → ℕ,      (∀ i : Fin r, 0 < I₁ i ∧ I₁ i + k ≤ I₂ i + 1) →        (∀ i j : Fin r, i < j → I₂ i < I₁ j) →          ¬ IsPower (∏ i : Fin r, ∏ m ∈ Icc (I₁ i) (I₂ i), m) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/930background